{"id":10441,"date":"2017-05-26T20:38:39","date_gmt":"2017-05-26T20:38:39","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10441"},"modified":"2024-04-30T16:42:46","modified_gmt":"2024-04-30T16:42:46","slug":"solving-discount-and-markup-applications","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/solving-discount-and-markup-applications\/","title":{"raw":"Solving Discount and Markup Applications","rendered":"Solving Discount and Markup Applications"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Solve discount applications<\/li>\r\n \t<li>Solve mark-up applications<\/li>\r\n<\/ul>\r\n<\/div>\r\nApplications of discount are very common in retail settings (see the image below). When you buy an item on sale, the <strong>original price<\/strong> of the item has been reduced by some dollar amount. The <strong>discount rate<\/strong>, usually given as a percent, is used to determine the amount of the discount. To determine the <strong>amount of discount<\/strong>, we multiply the discount rate by the original price. We summarize the discount model in the box below.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"450\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222045\/CNX_BMath_Figure_06_03_002.png\" alt=\"The figure shows a sale sign with a discount rate\" width=\"450\" height=\"301\" \/> Applications of discounts are common in everyday life. (credit: Charleston's TheDigitel, Flickr)[\/caption]\r\n\r\n<div class=\"textbox shaded\">\r\n<h3>Discount<\/h3>\r\nAn amount of discount is a percent off the original price.\r\n\r\n[latex]\\begin{array}{ccc}\\hfill \\text{amount of discount}&amp; =&amp; \\text{discount rate}\\cdot \\text{original price}\\hfill \\\\ \\hfill \\text{sale price}&amp; =&amp; \\text{original price}-\\text{discount}\\hfill \\end{array}[\/latex]\r\n\r\n<\/div>\r\nThe sale price should always be less than the original price. In some cases, the amount of discount is a fixed dollar amount. Then we just find the sale price by subtracting the amount of discount from the original price.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nJason bought a pair of sunglasses that were on sale for [latex]\\text{\\$10}[\/latex] off. The original price of the sunglasses was [latex]\\text{\\$39}[\/latex]. What was the sale price of the sunglasses?\r\n\r\nSolution\r\n<table id=\"eip-id1168469821476\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solving the problem. It shows seven steps. Identify what are asked to find: What is the sale price? Choose a variable to represent it: Let the variable s be equal to the sale price. Write a sentence that gives the information to find it: The sale price is the original price minus the discount. Translate into an equation: The sale price is represented by the variable s. The word 'is' is represented with an equal sign. The original price, $39, is written as 39. The word 'minus' is represented with a minus sign. The discount, $10, is written as 10. The equation is s = 39 - 10. Simplify: s = 29. Write a complete sentence that answers the question: The sale price of the sunglasses was $29. Check of this answer is reasonable: Yes. The sale price, $29, is less than the original price, $39.\">\r\n<tbody>\r\n<tr>\r\n<td>Identify what you are asked to find.<\/td>\r\n<td>What is the sale price?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Choose a variable to represent it.<\/td>\r\n<td>Let [latex]s=[\/latex] the sale price.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence that gives the information to find it.<\/td>\r\n<td>The sale price is the original price minus the discount.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate into an equation.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222047\/CNX_BMath_Figure_06_03_018_img-01.png\" alt=\"&quot;The sale price is the original 39 dollars price minus the 10 dollars discount\u201d can be translated to s equal 39 minus 10. The parts of the sentence translate as follows: \u201cThe sale price\u201d can be translated to \u201cs\u201d, the word \u201cis\u201d becomes an equal sign, &quot;the original 39 dollars price&quot; translates to 39, \u201cminus\u201d translates to subtraction, and &quot;the 10 dollars discount&quot; becomes 10.\" width=\"425\" height=\"76\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]s=29[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check if this answer is reasonable.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Yes. The sale price, [latex]\\text{\\$29}[\/latex], is less than the original price, [latex]\\text{\\$39}[\/latex].<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence that answers the question.<\/td>\r\n<td>The sale price of the sunglasses was [latex]\\text{\\$29}[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146772[\/ohm_question]\r\n\r\n<\/div>\r\nIn the first example, the amount of discount was a set amount, [latex]\\text{\\$10}[\/latex]. In the next example, the discount is given as a percent of the original price.\r\n<div class=\"textbox exercises\">\r\n<h3>exmaple<\/h3>\r\nElise bought a dress that was discounted [latex]\\text{35%}[\/latex] off of the original price of [latex]\\text{\\$140}[\/latex]. What was \u24d0 the amount of discount and \u24d1 the sale price of the dress?\r\n[reveal-answer q=\"967374\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"967374\"]\r\n\r\nSolution\r\n\u24d0 Before beginning, you may find it helpful to organize the information in a list.\r\n\r\nOriginal price = [latex]\\text{\\$140}[\/latex]\r\n\r\nDiscount rate = [latex]35\\text{%}[\/latex]\r\n\r\nAmount of discount = ?\r\n<table id=\"eip-id1168466735001\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solving part A. It shows seven steps. Identify what are asked to find: What is the amount of the discount? Choose a variable to represent it: Let the variable d be equal to the amount of the discount. Write a sentence that gives the information to find it: The discount is 35% of the original price. Translate into an equation: The discount is represented by the variable d. The word 'is' is represented with an equal sign. 35% is written as 0.35. The word 'of' is represented with a multiplication dot. The original price, 40, is written as 140. The equation is d = 0.35 \u00b7 140. Simplify: d = 49. Write a complete sentence that answers the question: The amount of the discount was $49. Check if this answer is reasonable: Yes. A $49 discount is reasonable for a 40 dress.\">\r\n<tbody>\r\n<tr>\r\n<td>Identify what you are asked to find.<\/td>\r\n<td>What is the amount of discount?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Choose a variable to represent it.<\/td>\r\n<td>Let [latex]d=[\/latex] the amount of discount.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence that gives the information to find it.<\/td>\r\n<td>The discount is [latex]35\\text{%}[\/latex] of the original price.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate into an equation.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222051\/CNX_BMath_Figure_06_03_019_img-01.png\" alt=\"&quot;The discount is 35% of the 140 dollars original price\u201d can be translated to s equals 0.35 times 140. The parts of the sentence translate as follows: \u201cThe discount\u201d can be translated to \u201cs\u201d, the word \u201cis\u201d becomes an equal sign, &quot; 35%&quot; becomes 0.35, \u201cof\u201d translates to multiplication, and &quot;the 140 dollars original price&quot; becomes 140.\" width=\"374\" height=\"76\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]d=49[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check if this answer is reasonable.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Yes. A [latex]\\text{\\$49}[\/latex] discount is reasonable for a [latex]\\text{\\$140}[\/latex] dress.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence that answers the question.<\/td>\r\n<td>The amount of discount was [latex]\\text{\\$49}[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\u24d1\r\n\r\nOriginal price = [latex]\\text{\\$140}[\/latex]\r\n\r\nAmount of discount = [latex]\\text{\\$49}[\/latex]\r\n\r\nSale price = ?\r\n<table id=\"eip-id1168468275547\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps for solving part B. It shows seven steps. Identify what you are asked to find: What is the sale price of the dress? Choose a variable to represent it: Let the variable s be equal to the sale price. Write a sentence that gives the information to find it: The sale price is the original price minus the discount. Translate into an equation: The sale price is represented by s. The word 'is' is represented with an equals sign. 40 is written as 140. The word 'minus' is represented with a minus sign. The amount of the discount, $49, is written as 49. The equation is s = 140 - 49. Simplify: s= 91. Write a complete sentence that answers the question: The sale price of the dress was $91. Check of this answer is reasonable: Yes. The sale price, $91, is less than the original price, 40.\">\r\n<tbody>\r\n<tr>\r\n<td>Identify what you are asked to find.<\/td>\r\n<td>What is the sale price of the dress?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Choose a variable to represent it.<\/td>\r\n<td>Let [latex]s=[\/latex] the sale price.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence that gives the information to find it.<\/td>\r\n<td>The sale price is the original price minus the discount.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate into an equation.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222055\/CNX_BMath_Figure_06_03_020_img-01.png\" alt=\"&quot;The sale price is the 140 dollars minus the 49 dollars discount\u201d can be translated to s equals 140 minus 49. The parts of the sentence translate as follows: \u201cThe sale price\u201d can be translated to \u201cs\u201d, the word \u201cis\u201d becomes an equal sign, &quot;the 140 dollars&quot; translates to 140, \u201cminus\u201d translates to subtraction, and &quot;the 49 dollars discount&quot; becomes 49.\" width=\"390\" height=\"76\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]s=91[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check if this answer is reasonable.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Yes. The sale price, [latex]\\text{\\$91}[\/latex], is less than the original price, [latex]\\text{\\$140}[\/latex].<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence that answers the question.<\/td>\r\n<td>The sale price of the dress was [latex]\\text{\\$91}[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146775[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nJeff has a coupon at the Guitar Store for [latex]15\\%[\/latex] off any purchase of [latex]\\$100[\/latex] or more. He wants to buy a used guitar that has a price tag of [latex]\\$220[\/latex] on it. Jeff wonders how much money the coupon will take off of the \u00a0[latex]\\$220[\/latex] original price<i>.<\/i>\r\n\r\n[reveal-answer q=\"285084\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"285084\"]Simplify the problems by eliminating extra words.\r\n<p style=\"text-align: center;\">How much is [latex]15\\%[\/latex] of [latex]$220[\/latex]?<\/p>\r\nIdentify the percent, the base, and the amount.\r\n\r\nPercent: \u00a0[latex]15\\%[\/latex]\r\nBase: \u00a0[latex]220[\/latex]\r\nAmount:\u00a0[latex]n[\/latex]\r\n\r\nWrite the percent equation.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}\\text{Percent}\\cdot\\text{Base}=\\text{Amount}\\\\15\\%\\cdot220=n\\end{array}[\/latex]<\/p>\r\nConvert \u00a0[latex]15\\%[\/latex] to [latex]0.15[\/latex], then multiply by [latex]220[\/latex]. \u00a0[latex]15\\%[\/latex] of [latex]$220[\/latex] is \u00a0[latex]$33[\/latex].\r\n<p style=\"text-align: center;\">[latex]0.15\\cdot220=33[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\nThe coupon will take [latex]$33[\/latex] off the original price.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nYou can estimate to see if the answer is reasonable. Since \u00a0[latex]15\\%[\/latex] is half way between \u00a0[latex]10\\%[\/latex] and [latex]20\\%[\/latex], find these numbers.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}10\\%\\,\\,\\text{of}\\,\\,220=0.1\\cdot220=22\\\\20\\%\\,\\,\\text{of}\\,\\,220=0.2\\cdot220=44\\end{array}[\/latex]<\/p>\r\nThe answer, [latex]33[\/latex], is between [latex]22[\/latex] and [latex]44[\/latex]. So [latex]$33[\/latex] seems reasonable.\r\n\r\nThe example video that follows shows how to use the percent equation to find the amount of a discount from the price of a phone.\r\n\r\nhttps:\/\/youtu.be\/bC7GUc1K6LU\r\n<h3>Calculate Discount Rate<\/h3>\r\nThere may be times when you buy something on sale and want to know the discount rate. The next example will show this case.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nJeannette bought a swimsuit at a sale price of [latex]\\text{\\$13.95}[\/latex]. The original price of the swimsuit was [latex]\\text{\\$31}[\/latex]. Find \u24d0 the amount of discount and \u24d1 the discount rate.\r\n[reveal-answer q=\"123339\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"123339\"]\r\n\r\nSolution\r\n\u24d0 Before beginning, you may find it helpful to organize the information in a list.\r\n\r\nOriginal price = [latex]\\text{\\$31}[\/latex]\r\n\r\nAmount of discount = ?\r\n\r\nSale price = [latex]\\text{\\$13.95}[\/latex]\r\n<table id=\"eip-id1168466277396\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solving part A. It shows seven steps. Identify what you are asked to find: What is the amount of the discount? Choose a variable to represent it: Let the variable d be equal to the amount of the discount. Write a sentence that gives the information to find it: The discount is the original price minus the sale price. Translate into an equation: The amount of the discount is represented by d. The word 'is' is represented with an equals sign. The original price, &gt;1, is written as 31 . The word 'minus' is represented with a minus sign. The sale price, 3.95, is written as 13.95. The equation is d = 31 - 13.95. Simplify: d = 17.05. Write a complete sentence that answers the question: The amount of the discount was 7.05. Check if this answer is reasonable: Yes. The 7.05 discount is less than the original price.\">\r\n<tbody>\r\n<tr>\r\n<td>Identify what you are asked to find.<\/td>\r\n<td>What is the amount of discount?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Choose a variable to represent it.<\/td>\r\n<td>Let [latex]d=[\/latex] the amount of discount.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence that gives the information to find it.<\/td>\r\n<td>The discount is the original price minus the sale price.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate into an equation.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222059\/CNX_BMath_Figure_06_03_021_img-01.png\" alt=\"&quot;The discount is the 31 dollars original price minus the 13.95 dollars sale price\u201d can be translated to s equals 31 minus 13.95. The parts of the sentence translate as follows: \u201cThe discount&quot; can be translated to \u201cs\u201d, the word \u201cis\u201d becomes an equal sign, &quot;the 31 dollars original price&quot; translates to 31, \u201cminus\u201d translates to subtraction, and &quot;the 13.95 dollars sale price&quot; becomes 13.95.\" width=\"444\" height=\"76\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]d=17.05[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check if this answer is reasonable.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Yes. The [latex]\\text{\\$17.05}[\/latex] discount is less than the original price.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence that answers the question.<\/td>\r\n<td>The amount of discount was [latex]$17.05[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\u24d1 Before beginning, you may find it helpful to organize the information in a list.\r\n\r\nOriginal price = [latex]$31[\/latex]\r\n\r\nAmount of discount = [latex]$17.05[\/latex]\r\n\r\nDiscount rate = ?\r\n<table id=\"eip-id1168469568385\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps for solving part B. It shows eight steps. Identify what you are asked to find: What is the discount rate? Choose a variable to represent it: Let the variable r be equal to the discount rate. Write a sentence that gives the information to find it: The discount what percent of the original price? The discount of 7.05 is written as 17.05. The word 'is' is represented with an equals sign. The percent is represented by r. The word 'of' is represented with a multiplication dot. The original price, &gt;1, is written as 31. The equation is 17.05 is equal to r times 31. Divide: 17.05 divided by 31 is equal to the product of r and 31 divided by 31. Simplify: 0.55 is equal to r. Write a complete sentence that answers the question: The rate of discount was 55%. Check if this answer is reasonable: The rate of discount was a little mote than 50%, and the amount of discount is a little more than half of &gt;1.\">\r\n<tbody>\r\n<tr>\r\n<td>Identify what you are asked to find.<\/td>\r\n<td>What is the discount rate?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Choose a variable to represent it.<\/td>\r\n<td>Let [latex]r=[\/latex] the discount rate.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence that gives the information to find it.<\/td>\r\n<td>The discount is what percent of the original price?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate into an equation.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222103\/CNX_BMath_Figure_06_03_022_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide.<\/td>\r\n<td>[latex]\\Large\\frac{17.05}{31}\\normalsize =\\Large\\frac{r(31)}{31}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]0.55=r[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check if this answer is reasonable.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The rate of discount was a little more than [latex]50\\text{%}[\/latex] and the amount of discount is a little more than half of [latex]\\text{\\$31}[\/latex].<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence that answers the question.<\/td>\r\n<td>The rate of discount was [latex]55\\text{%}[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146777[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show another example of how to find the discount rate (also called the percent of change) given the original price and the marked-down price.\r\n\r\nhttps:\/\/youtu.be\/gH7XJFdMsRc\r\n<h2>Solve Mark-up Applications<\/h2>\r\nApplications of mark-up are very common in retail settings. The price a retailer pays for an item is called the <strong>wholesale price<\/strong>. The retailer then adds a <strong>mark-up<\/strong> to the wholesale price to get the <strong>list price<\/strong>, the price he sells the item for. The mark-up is usually calculated as a percent of the wholesale price. The percent is called the <strong>mark-up rate<\/strong>. To determine the amount of mark-up, multiply the mark-up rate by the wholesale price. We summarize the mark-up model in the box below.\r\n<div class=\"textbox shaded\">\r\n<h3>Mark-up<\/h3>\r\nThe mark-up is the amount added to the wholesale price.\r\n\r\n[latex]\\begin{array}{ccc}\\hfill \\text{amount of mark-up}&amp; =&amp; \\text{mark-up rate}\\cdot \\text{wholesale price}\\hfill \\\\ \\hfill \\text{list price}&amp; =&amp; \\text{wholesale price}+\\text{mark up}\\hfill \\end{array}[\/latex]\r\n\r\nThe list price should always be more than the wholesale price.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAdam's art gallery bought a photograph at the wholesale price of [latex]\\text{\\$250}[\/latex]. Adam marked the price up [latex]\\text{40%}[\/latex]. Find \u24d0 the amount of mark-up and \u24d1 the list price of the photograph.\r\n[reveal-answer q=\"661316\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"661316\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468667368\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps for solving part B. It shows eight steps. Identify what you are asked to find: What is the discount rate? Choose a variable to represent it: Let the variable r be equal to the discount rate. Write a sentence that gives the information to find it: The discount what percent of the original price? The discount of 7.05 is written as 17.05. The word 'is' is represented with an equals sign. The percent is represented by r. The word 'of' is represented with a multiplication dot. The original price, &gt;1, is written as 31. The equation is 17.05 is equal to r times 31. Divide: 17.05 divided by 31 is equal to the product of r and 31 divided by 31. Simplify: 0.55 is equal to r. Write a complete sentence that answers the question: The rate of discount was 55%. Check if this answer is reasonable: The rate of discount was a little mote than 50%, and the amount of discount is a little more than half of &gt;1.\">\r\n<tbody>\r\n<tr>\r\n<td>\u24d0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Identify what you are asked to find.<\/td>\r\n<td>What is the amount of mark-up?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Choose a variable to represent it.<\/td>\r\n<td>Let [latex]m=[\/latex] the amount of each mark-up.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence that gives the information to find it.<\/td>\r\n<td>The mark-up is [latex]40\\text{%}[\/latex] of the wholesale price.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate into an equation.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222110\/CNX_BMath_Figure_06_03_023_img-01.png\" alt=\"&quot;The markup is 40 percent of the 250 dollars wholesale price\u201d can be translated to m equals 0.40 times 250. The parts of the sentence translate as follows: \u201cThe markup\u201d can be translated to \u201cm\u201d, the word \u201cis\u201d becomes an equal sign, &quot;40%&quot; translates to 0.40, \u201cof\u201d translates to multiplication, and &quot;the 250 dollars wholesale price&quot; becomes 250.\" width=\"389\" height=\"71\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]m=100[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check if this answer is reasonable.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Yes. The markup rate is less than [latex]50\\text{%}[\/latex] and [latex]\\text{\\$100}[\/latex] is less than half of [latex]\\text{\\$250}[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence that answers the question.<\/td>\r\n<td>The mark-up on the photograph was [latex]\\text{\\$100}[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168467213810\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps for solving part B. It shows seven steps. Identify what you are asked to find: What is the list price? Choose a variable to represent it: Let the variable p be equal to the list price. Write a sentence that gives the information to find it: The list price is the wholesale price plus the mark-up. Translate into an equation: Let the list price be represented by p. The word 'is' is represented with an equals sign. The wholesale price, $250, is written as 250. The word 'plus' is represented with an addition sign. The $100 mark-up is written as 100. The equation is p = 250 + 100. Simplify: p is = 350. Write a complete sentence that answers the question: The list price of the photograph was $350. Check if this answer is reasonable: Yes. The list price, $350, is more than the wholesale price, $250.\">\r\n<tbody>\r\n<tr>\r\n<td>\u24d1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Identify what you are asked to find.<\/td>\r\n<td>What is the list price?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Choose a variable to represent it.<\/td>\r\n<td>Let [latex]p=[\/latex] the list price.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence that gives the information to find it.<\/td>\r\n<td>The list price is the wholesale price plus the mark-up.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate into an equation.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222114\/CNX_BMath_Figure_06_03_024_img-01.png\" alt=\"&quot;The list price is the 250 dollars wholesale price plus the 100 dollars mark-up\u201d can be translated to p equals 250 plus 100. The parts of the sentence translate as follows: \u201cThe list price\u201d can be translated to \u201cp\u201d, the word \u201cis\u201d becomes an equal sign, &quot;the 250 dollars wholesale price&quot; translates to 250, \u201cplus\u201d translates to addition, and &quot;the 100 dollars mark-up&quot; becomes 100.\" width=\"437\" height=\"71\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]p=350[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check if this answer is reasonable.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Yes. The list price, [latex]\\text{\\$350}[\/latex], is more than the wholesale price, [latex]\\text{\\$250}[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence that answers the question.<\/td>\r\n<td>The list price of the photograph was [latex]\\text{\\$350}[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146778[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Solve discount applications<\/li>\n<li>Solve mark-up applications<\/li>\n<\/ul>\n<\/div>\n<p>Applications of discount are very common in retail settings (see the image below). When you buy an item on sale, the <strong>original price<\/strong> of the item has been reduced by some dollar amount. The <strong>discount rate<\/strong>, usually given as a percent, is used to determine the amount of the discount. To determine the <strong>amount of discount<\/strong>, we multiply the discount rate by the original price. We summarize the discount model in the box below.<\/p>\n<div style=\"width: 460px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222045\/CNX_BMath_Figure_06_03_002.png\" alt=\"The figure shows a sale sign with a discount rate\" width=\"450\" height=\"301\" \/><\/p>\n<p class=\"wp-caption-text\">Applications of discounts are common in everyday life. (credit: Charleston&#8217;s TheDigitel, Flickr)<\/p>\n<\/div>\n<div class=\"textbox shaded\">\n<h3>Discount<\/h3>\n<p>An amount of discount is a percent off the original price.<\/p>\n<p>[latex]\\begin{array}{ccc}\\hfill \\text{amount of discount}& =& \\text{discount rate}\\cdot \\text{original price}\\hfill \\\\ \\hfill \\text{sale price}& =& \\text{original price}-\\text{discount}\\hfill \\end{array}[\/latex]<\/p>\n<\/div>\n<p>The sale price should always be less than the original price. In some cases, the amount of discount is a fixed dollar amount. Then we just find the sale price by subtracting the amount of discount from the original price.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Jason bought a pair of sunglasses that were on sale for [latex]\\text{\\$10}[\/latex] off. The original price of the sunglasses was [latex]\\text{\\$39}[\/latex]. What was the sale price of the sunglasses?<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168469821476\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solving the problem. It shows seven steps. Identify what are asked to find: What is the sale price? Choose a variable to represent it: Let the variable s be equal to the sale price. Write a sentence that gives the information to find it: The sale price is the original price minus the discount. Translate into an equation: The sale price is represented by the variable s. The word 'is' is represented with an equal sign. The original price, $39, is written as 39. The word 'minus' is represented with a minus sign. The discount, $10, is written as 10. The equation is s = 39 - 10. Simplify: s = 29. Write a complete sentence that answers the question: The sale price of the sunglasses was $29. Check of this answer is reasonable: Yes. The sale price, $29, is less than the original price, $39.\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>What is the sale price?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]s=[\/latex] the sale price.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>The sale price is the original price minus the discount.<\/td>\n<\/tr>\n<tr>\n<td>Translate into an equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222047\/CNX_BMath_Figure_06_03_018_img-01.png\" alt=\"&quot;The sale price is the original 39 dollars price minus the 10 dollars discount\u201d can be translated to s equal 39 minus 10. The parts of the sentence translate as follows: \u201cThe sale price\u201d can be translated to \u201cs\u201d, the word \u201cis\u201d becomes an equal sign, &quot;the original 39 dollars price&quot; translates to 39, \u201cminus\u201d translates to subtraction, and &quot;the 10 dollars discount&quot; becomes 10.\" width=\"425\" height=\"76\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]s=29[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check if this answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. The sale price, [latex]\\text{\\$29}[\/latex], is less than the original price, [latex]\\text{\\$39}[\/latex].<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The sale price of the sunglasses was [latex]\\text{\\$29}[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146772\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146772&theme=oea&iframe_resize_id=ohm146772&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the first example, the amount of discount was a set amount, [latex]\\text{\\$10}[\/latex]. In the next example, the discount is given as a percent of the original price.<\/p>\n<div class=\"textbox exercises\">\n<h3>exmaple<\/h3>\n<p>Elise bought a dress that was discounted [latex]\\text{35%}[\/latex] off of the original price of [latex]\\text{\\$140}[\/latex]. What was \u24d0 the amount of discount and \u24d1 the sale price of the dress?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q967374\">Show Solution<\/span><\/p>\n<div id=\"q967374\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\n\u24d0 Before beginning, you may find it helpful to organize the information in a list.<\/p>\n<p>Original price = [latex]\\text{\\$140}[\/latex]<\/p>\n<p>Discount rate = [latex]35\\text{%}[\/latex]<\/p>\n<p>Amount of discount = ?<\/p>\n<table id=\"eip-id1168466735001\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solving part A. It shows seven steps. Identify what are asked to find: What is the amount of the discount? Choose a variable to represent it: Let the variable d be equal to the amount of the discount. Write a sentence that gives the information to find it: The discount is 35% of the original price. Translate into an equation: The discount is represented by the variable d. The word 'is' is represented with an equal sign. 35% is written as 0.35. The word 'of' is represented with a multiplication dot. The original price, 40, is written as 140. The equation is d = 0.35 \u00b7 140. Simplify: d = 49. Write a complete sentence that answers the question: The amount of the discount was $49. Check if this answer is reasonable: Yes. A $49 discount is reasonable for a 40 dress.\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>What is the amount of discount?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]d=[\/latex] the amount of discount.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>The discount is [latex]35\\text{%}[\/latex] of the original price.<\/td>\n<\/tr>\n<tr>\n<td>Translate into an equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222051\/CNX_BMath_Figure_06_03_019_img-01.png\" alt=\"&quot;The discount is 35% of the 140 dollars original price\u201d can be translated to s equals 0.35 times 140. The parts of the sentence translate as follows: \u201cThe discount\u201d can be translated to \u201cs\u201d, the word \u201cis\u201d becomes an equal sign, &quot; 35%&quot; becomes 0.35, \u201cof\u201d translates to multiplication, and &quot;the 140 dollars original price&quot; becomes 140.\" width=\"374\" height=\"76\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]d=49[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check if this answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. A [latex]\\text{\\$49}[\/latex] discount is reasonable for a [latex]\\text{\\$140}[\/latex] dress.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The amount of discount was [latex]\\text{\\$49}[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u24d1<\/p>\n<p>Original price = [latex]\\text{\\$140}[\/latex]<\/p>\n<p>Amount of discount = [latex]\\text{\\$49}[\/latex]<\/p>\n<p>Sale price = ?<\/p>\n<table id=\"eip-id1168468275547\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps for solving part B. It shows seven steps. Identify what you are asked to find: What is the sale price of the dress? Choose a variable to represent it: Let the variable s be equal to the sale price. Write a sentence that gives the information to find it: The sale price is the original price minus the discount. Translate into an equation: The sale price is represented by s. The word 'is' is represented with an equals sign. 40 is written as 140. The word 'minus' is represented with a minus sign. The amount of the discount, $49, is written as 49. The equation is s = 140 - 49. Simplify: s= 91. Write a complete sentence that answers the question: The sale price of the dress was $91. Check of this answer is reasonable: Yes. The sale price, $91, is less than the original price, 40.\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>What is the sale price of the dress?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]s=[\/latex] the sale price.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>The sale price is the original price minus the discount.<\/td>\n<\/tr>\n<tr>\n<td>Translate into an equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222055\/CNX_BMath_Figure_06_03_020_img-01.png\" alt=\"&quot;The sale price is the 140 dollars minus the 49 dollars discount\u201d can be translated to s equals 140 minus 49. The parts of the sentence translate as follows: \u201cThe sale price\u201d can be translated to \u201cs\u201d, the word \u201cis\u201d becomes an equal sign, &quot;the 140 dollars&quot; translates to 140, \u201cminus\u201d translates to subtraction, and &quot;the 49 dollars discount&quot; becomes 49.\" width=\"390\" height=\"76\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]s=91[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check if this answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. The sale price, [latex]\\text{\\$91}[\/latex], is less than the original price, [latex]\\text{\\$140}[\/latex].<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The sale price of the dress was [latex]\\text{\\$91}[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146775\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146775&theme=oea&iframe_resize_id=ohm146775&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Jeff has a coupon at the Guitar Store for [latex]15\\%[\/latex] off any purchase of [latex]\\$100[\/latex] or more. He wants to buy a used guitar that has a price tag of [latex]\\$220[\/latex] on it. Jeff wonders how much money the coupon will take off of the \u00a0[latex]\\$220[\/latex] original price<i>.<\/i><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q285084\">Show Solution<\/span><\/p>\n<div id=\"q285084\" class=\"hidden-answer\" style=\"display: none\">Simplify the problems by eliminating extra words.<\/p>\n<p style=\"text-align: center;\">How much is [latex]15\\%[\/latex] of [latex]$220[\/latex]?<\/p>\n<p>Identify the percent, the base, and the amount.<\/p>\n<p>Percent: \u00a0[latex]15\\%[\/latex]<br \/>\nBase: \u00a0[latex]220[\/latex]<br \/>\nAmount:\u00a0[latex]n[\/latex]<\/p>\n<p>Write the percent equation.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}\\text{Percent}\\cdot\\text{Base}=\\text{Amount}\\\\15\\%\\cdot220=n\\end{array}[\/latex]<\/p>\n<p>Convert \u00a0[latex]15\\%[\/latex] to [latex]0.15[\/latex], then multiply by [latex]220[\/latex]. \u00a0[latex]15\\%[\/latex] of [latex]$220[\/latex] is \u00a0[latex]$33[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]0.15\\cdot220=33[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>The coupon will take [latex]$33[\/latex] off the original price.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>You can estimate to see if the answer is reasonable. Since \u00a0[latex]15\\%[\/latex] is half way between \u00a0[latex]10\\%[\/latex] and [latex]20\\%[\/latex], find these numbers.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}10\\%\\,\\,\\text{of}\\,\\,220=0.1\\cdot220=22\\\\20\\%\\,\\,\\text{of}\\,\\,220=0.2\\cdot220=44\\end{array}[\/latex]<\/p>\n<p>The answer, [latex]33[\/latex], is between [latex]22[\/latex] and [latex]44[\/latex]. So [latex]$33[\/latex] seems reasonable.<\/p>\n<p>The example video that follows shows how to use the percent equation to find the amount of a discount from the price of a phone.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Percent App:  Find the Amount of Savings from a Discount\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/bC7GUc1K6LU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3>Calculate Discount Rate<\/h3>\n<p>There may be times when you buy something on sale and want to know the discount rate. The next example will show this case.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Jeannette bought a swimsuit at a sale price of [latex]\\text{\\$13.95}[\/latex]. The original price of the swimsuit was [latex]\\text{\\$31}[\/latex]. Find \u24d0 the amount of discount and \u24d1 the discount rate.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q123339\">Show Solution<\/span><\/p>\n<div id=\"q123339\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\n\u24d0 Before beginning, you may find it helpful to organize the information in a list.<\/p>\n<p>Original price = [latex]\\text{\\$31}[\/latex]<\/p>\n<p>Amount of discount = ?<\/p>\n<p>Sale price = [latex]\\text{\\$13.95}[\/latex]<\/p>\n<table id=\"eip-id1168466277396\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solving part A. It shows seven steps. Identify what you are asked to find: What is the amount of the discount? Choose a variable to represent it: Let the variable d be equal to the amount of the discount. Write a sentence that gives the information to find it: The discount is the original price minus the sale price. Translate into an equation: The amount of the discount is represented by d. The word 'is' is represented with an equals sign. The original price, &gt;1, is written as 31 . The word 'minus' is represented with a minus sign. The sale price, 3.95, is written as 13.95. The equation is d = 31 - 13.95. Simplify: d = 17.05. Write a complete sentence that answers the question: The amount of the discount was 7.05. Check if this answer is reasonable: Yes. The 7.05 discount is less than the original price.\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>What is the amount of discount?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]d=[\/latex] the amount of discount.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>The discount is the original price minus the sale price.<\/td>\n<\/tr>\n<tr>\n<td>Translate into an equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222059\/CNX_BMath_Figure_06_03_021_img-01.png\" alt=\"&quot;The discount is the 31 dollars original price minus the 13.95 dollars sale price\u201d can be translated to s equals 31 minus 13.95. The parts of the sentence translate as follows: \u201cThe discount&quot; can be translated to \u201cs\u201d, the word \u201cis\u201d becomes an equal sign, &quot;the 31 dollars original price&quot; translates to 31, \u201cminus\u201d translates to subtraction, and &quot;the 13.95 dollars sale price&quot; becomes 13.95.\" width=\"444\" height=\"76\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]d=17.05[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check if this answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. The [latex]\\text{\\$17.05}[\/latex] discount is less than the original price.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The amount of discount was [latex]$17.05[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u24d1 Before beginning, you may find it helpful to organize the information in a list.<\/p>\n<p>Original price = [latex]$31[\/latex]<\/p>\n<p>Amount of discount = [latex]$17.05[\/latex]<\/p>\n<p>Discount rate = ?<\/p>\n<table id=\"eip-id1168469568385\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps for solving part B. It shows eight steps. Identify what you are asked to find: What is the discount rate? Choose a variable to represent it: Let the variable r be equal to the discount rate. Write a sentence that gives the information to find it: The discount what percent of the original price? The discount of 7.05 is written as 17.05. The word 'is' is represented with an equals sign. The percent is represented by r. The word 'of' is represented with a multiplication dot. The original price, &gt;1, is written as 31. The equation is 17.05 is equal to r times 31. Divide: 17.05 divided by 31 is equal to the product of r and 31 divided by 31. Simplify: 0.55 is equal to r. Write a complete sentence that answers the question: The rate of discount was 55%. Check if this answer is reasonable: The rate of discount was a little mote than 50%, and the amount of discount is a little more than half of &gt;1.\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>What is the discount rate?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]r=[\/latex] the discount rate.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>The discount is what percent of the original price?<\/td>\n<\/tr>\n<tr>\n<td>Translate into an equation.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222103\/CNX_BMath_Figure_06_03_022_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td>[latex]\\Large\\frac{17.05}{31}\\normalsize =\\Large\\frac{r(31)}{31}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]0.55=r[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check if this answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The rate of discount was a little more than [latex]50\\text{%}[\/latex] and the amount of discount is a little more than half of [latex]\\text{\\$31}[\/latex].<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The rate of discount was [latex]55\\text{%}[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146777\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146777&theme=oea&iframe_resize_id=ohm146777&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show another example of how to find the discount rate (also called the percent of change) given the original price and the marked-down price.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Example 1:  Determine a Percent of Change  (decrease)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/gH7XJFdMsRc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Solve Mark-up Applications<\/h2>\n<p>Applications of mark-up are very common in retail settings. The price a retailer pays for an item is called the <strong>wholesale price<\/strong>. The retailer then adds a <strong>mark-up<\/strong> to the wholesale price to get the <strong>list price<\/strong>, the price he sells the item for. The mark-up is usually calculated as a percent of the wholesale price. The percent is called the <strong>mark-up rate<\/strong>. To determine the amount of mark-up, multiply the mark-up rate by the wholesale price. We summarize the mark-up model in the box below.<\/p>\n<div class=\"textbox shaded\">\n<h3>Mark-up<\/h3>\n<p>The mark-up is the amount added to the wholesale price.<\/p>\n<p>[latex]\\begin{array}{ccc}\\hfill \\text{amount of mark-up}& =& \\text{mark-up rate}\\cdot \\text{wholesale price}\\hfill \\\\ \\hfill \\text{list price}& =& \\text{wholesale price}+\\text{mark up}\\hfill \\end{array}[\/latex]<\/p>\n<p>The list price should always be more than the wholesale price.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Adam&#8217;s art gallery bought a photograph at the wholesale price of [latex]\\text{\\$250}[\/latex]. Adam marked the price up [latex]\\text{40%}[\/latex]. Find \u24d0 the amount of mark-up and \u24d1 the list price of the photograph.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q661316\">Show Solution<\/span><\/p>\n<div id=\"q661316\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468667368\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps for solving part B. It shows eight steps. Identify what you are asked to find: What is the discount rate? Choose a variable to represent it: Let the variable r be equal to the discount rate. Write a sentence that gives the information to find it: The discount what percent of the original price? The discount of 7.05 is written as 17.05. The word 'is' is represented with an equals sign. The percent is represented by r. The word 'of' is represented with a multiplication dot. The original price, &gt;1, is written as 31. The equation is 17.05 is equal to r times 31. Divide: 17.05 divided by 31 is equal to the product of r and 31 divided by 31. Simplify: 0.55 is equal to r. Write a complete sentence that answers the question: The rate of discount was 55%. Check if this answer is reasonable: The rate of discount was a little mote than 50%, and the amount of discount is a little more than half of &gt;1.\">\n<tbody>\n<tr>\n<td>\u24d0<\/td>\n<\/tr>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>What is the amount of mark-up?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]m=[\/latex] the amount of each mark-up.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>The mark-up is [latex]40\\text{%}[\/latex] of the wholesale price.<\/td>\n<\/tr>\n<tr>\n<td>Translate into an equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222110\/CNX_BMath_Figure_06_03_023_img-01.png\" alt=\"&quot;The markup is 40 percent of the 250 dollars wholesale price\u201d can be translated to m equals 0.40 times 250. The parts of the sentence translate as follows: \u201cThe markup\u201d can be translated to \u201cm\u201d, the word \u201cis\u201d becomes an equal sign, &quot;40%&quot; translates to 0.40, \u201cof\u201d translates to multiplication, and &quot;the 250 dollars wholesale price&quot; becomes 250.\" width=\"389\" height=\"71\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]m=100[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check if this answer is reasonable.<\/td>\n<\/tr>\n<tr>\n<td>Yes. The markup rate is less than [latex]50\\text{%}[\/latex] and [latex]\\text{\\$100}[\/latex] is less than half of [latex]\\text{\\$250}[\/latex].<\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The mark-up on the photograph was [latex]\\text{\\$100}[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467213810\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps for solving part B. It shows seven steps. Identify what you are asked to find: What is the list price? Choose a variable to represent it: Let the variable p be equal to the list price. Write a sentence that gives the information to find it: The list price is the wholesale price plus the mark-up. Translate into an equation: Let the list price be represented by p. The word 'is' is represented with an equals sign. The wholesale price, $250, is written as 250. The word 'plus' is represented with an addition sign. The $100 mark-up is written as 100. The equation is p = 250 + 100. Simplify: p is = 350. Write a complete sentence that answers the question: The list price of the photograph was $350. Check if this answer is reasonable: Yes. The list price, $350, is more than the wholesale price, $250.\">\n<tbody>\n<tr>\n<td>\u24d1<\/td>\n<\/tr>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>What is the list price?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]p=[\/latex] the list price.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>The list price is the wholesale price plus the mark-up.<\/td>\n<\/tr>\n<tr>\n<td>Translate into an equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222114\/CNX_BMath_Figure_06_03_024_img-01.png\" alt=\"&quot;The list price is the 250 dollars wholesale price plus the 100 dollars mark-up\u201d can be translated to p equals 250 plus 100. The parts of the sentence translate as follows: \u201cThe list price\u201d can be translated to \u201cp\u201d, the word \u201cis\u201d becomes an equal sign, &quot;the 250 dollars wholesale price&quot; translates to 250, \u201cplus\u201d translates to addition, and &quot;the 100 dollars mark-up&quot; becomes 100.\" width=\"437\" height=\"71\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]p=350[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check if this answer is reasonable.<\/td>\n<\/tr>\n<tr>\n<td>Yes. The list price, [latex]\\text{\\$350}[\/latex], is more than the wholesale price, [latex]\\text{\\$250}[\/latex].<\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The list price of the photograph was [latex]\\text{\\$350}[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146778\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146778&theme=oea&iframe_resize_id=ohm146778&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-10441\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146778, 146777, 146775. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Example 1: Determine a Percent of Change (decrease). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/gH7XJFdMsRc\">https:\/\/youtu.be\/gH7XJFdMsRc<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Example 2: Determine a Percent of Change (increase). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/Bhqb1XOWcQQ\">https:\/\/youtu.be\/Bhqb1XOWcQQ<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":16,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Question ID 146778, 146777, 146775\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Example 1: Determine a Percent of Change (decrease)\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/gH7XJFdMsRc\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Example 2: Determine a Percent of Change (increase)\",\"author\":\"James Sousa 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