{"id":363,"date":"2018-04-17T02:23:45","date_gmt":"2018-04-17T02:23:45","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/?post_type=chapter&#038;p=363"},"modified":"2024-04-26T22:06:58","modified_gmt":"2024-04-26T22:06:58","slug":"discount-problems","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/chapter\/discount-problems\/","title":{"raw":"Discount Problems","rendered":"Discount Problems"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning outcome<\/h3>\r\n<ul>\r\n \t<li>Use mathematical notation to solve discount problems<\/li>\r\n<\/ul>\r\n<\/div>\r\n\r\n[caption id=\"attachment_891\" align=\"alignright\" width=\"463\"]<img class=\"wp-image-891\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2985\/2018\/04\/11185540\/Screen-Shot-2018-05-11-at-10.28.20-AM-e1526064962826-300x207.png\" alt=\"A bedroom setting\" width=\"463\" height=\"320\" \/> Feminine Furnishings Bedding Sale[\/caption]\r\n<p data-type=\"title\">A store called Feminine Furnishings is having a sale on bedding. Their queen sheet sets have a list price of [latex]$126[\/latex]. During the first two weeks of February, the store has a\u2014Snuggle Up In Love Sale\u2014 where customers save [latex]14\\%[\/latex] on any white, pink, or red bedding set. Carly selects a bedding set with pink stripes and pays [latex]$108.36[\/latex].<\/p>\r\n<p data-type=\"title\">Applications of discount are very common in retail settings. When you buy an item on sale, the <strong>original <\/strong>or<strong> list 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>\r\n\r\n<div class=\"textbox shaded\">\r\n<h3>Discount<\/h3>\r\nAn amount of discount is subtracted from the original price.\r\n<p style=\"padding-left: 60px;\"><strong>amount of discount = discount rate [latex]\\cdot[\/latex] original price<\/strong><\/p>\r\n<p style=\"padding-left: 60px;\"><strong>sale price = original price [latex]-[\/latex] discount<\/strong><\/p>\r\nThe sale price should always be less than the original price.\r\n\r\nIn 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. For example, as you walk into a store you may see a sign that says \"Spend [latex]$100[\/latex] or more, and receive a [latex]$20[\/latex] discount!\"\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nJason bought a pair of sunglasses from a rack that was labeled [latex]\\text{\\$10}[\/latex] off all Retrop brand glasses. The original price of the sunglasses was [latex]\\text{\\$39}[\/latex]. What was the sale price of the sunglasses?\r\n\r\n[reveal-answer q=\"967734\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"967734\"]\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.\" data-label=\"\">\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=\"The sale price is the original 39 dollar price minus the 10 dollar discount translates to s equals 39 minus 10. The phrase &quot;the sale price&quot; can be represented by s. The word &quot;is&quot; translates to the equals sign. The original 39 dollar price equates to 39. Minus correlates to subtraction. And the 10 dollar discount equates to 10.\" width=\"425\" height=\"76\" data-media-type=\"image\/png\" \/><\/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[\/hidden-answer]\r\n\r\n<\/div>\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 or static amount. In the next example, the discount is given as a percent of the original price.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/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 the amount of discount and the sale price of the dress?\r\n[reveal-answer q=\"967374\"]Show Answer[\/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.\" data-label=\"\">\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=\"The discount is 35 percent of the 140 dollar original price translates to the equation s equals 0.35 times 140. The discount can be represented by s. The word &quot;is&quot; translates to the equals sign. 35 percent becomes 0.35. The word &quot;of&quot; correlates to multiplication. The phrase &quot;the 140 dollar original price&quot; translates to 140.\" width=\"374\" height=\"76\" data-media-type=\"image\/png\" \/><\/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.\" data-label=\"\">\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=\"The sale price is the 140 dollars minus the 49 dollar discount translates to the equation s equals 140 minus 49. The sale price can be represented with s. The word &quot;is&quot; translates to the equals sign. The 140 dollars equates to 140. Minus correlates to subtraction. The 49 dollar discount translates to 49.\" width=\"390\" height=\"76\" data-media-type=\"image\/png\" \/><\/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<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146775[\/ohm_question]\r\n\r\n<\/div>\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 the \u24d0 amount of discount and \u24d1 discount rate.\r\n[reveal-answer q=\"123339\"]Show Answer[\/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.\" data-label=\"\">\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=\"The discount is the 31 dollar original price minus the 13.95 dollar sale price translates to the equation s equals 31 minus 13.95. The discount can be represented by s. The word &quot;is&quot; translates to the equals sign. The 31 dollar original price equates to 31. Minus correlates to subtraction. The 13.95 dollar sale price equates to 13.95.\" width=\"444\" height=\"76\" data-media-type=\"image\/png\" \/><\/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.\" data-label=\"\">\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 class=\"alignnone wp-image-3630 size-full\" src=\"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-content\/uploads\/sites\/2985\/2018\/04\/fixed-1.png\" alt=\"The discount of 17.05 dollars is what percent of the 31 dollar original price translates to the equation 17.05 equals r times 31. The discount of 17.05 dollars equates to 17.05. The word &quot;is&quot; translates to the equals sign. What percent can be represented by p. The word &quot;of&quot; correlates to multiplication. The 31 dollar original price equates to 31.\" width=\"221\" height=\"60\" \/><\/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<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]156971[\/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","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning outcome<\/h3>\n<ul>\n<li>Use mathematical notation to solve discount problems<\/li>\n<\/ul>\n<\/div>\n<div id=\"attachment_891\" style=\"width: 473px\" class=\"wp-caption alignright\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-891\" class=\"wp-image-891\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2985\/2018\/04\/11185540\/Screen-Shot-2018-05-11-at-10.28.20-AM-e1526064962826-300x207.png\" alt=\"A bedroom setting\" width=\"463\" height=\"320\" \/><\/p>\n<p id=\"caption-attachment-891\" class=\"wp-caption-text\">Feminine Furnishings Bedding Sale<\/p>\n<\/div>\n<p data-type=\"title\">A store called Feminine Furnishings is having a sale on bedding. Their queen sheet sets have a list price of [latex]$126[\/latex]. During the first two weeks of February, the store has a\u2014Snuggle Up In Love Sale\u2014 where customers save [latex]14\\%[\/latex] on any white, pink, or red bedding set. Carly selects a bedding set with pink stripes and pays [latex]$108.36[\/latex].<\/p>\n<p data-type=\"title\">Applications of discount are very common in retail settings. When you buy an item on sale, the <strong>original <\/strong>or<strong> list 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 class=\"textbox shaded\">\n<h3>Discount<\/h3>\n<p>An amount of discount is subtracted from the original price.<\/p>\n<p style=\"padding-left: 60px;\"><strong>amount of discount = discount rate [latex]\\cdot[\/latex] original price<\/strong><\/p>\n<p style=\"padding-left: 60px;\"><strong>sale price = original price [latex]-[\/latex] discount<\/strong><\/p>\n<p>The sale price should always be less than the original price.<\/p>\n<p>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. For example, as you walk into a store you may see a sign that says &#8220;Spend [latex]$100[\/latex] or more, and receive a [latex]$20[\/latex] discount!&#8221;<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Jason bought a pair of sunglasses from a rack that was labeled [latex]\\text{\\$10}[\/latex] off all Retrop brand glasses. The original price of the sunglasses was [latex]\\text{\\$39}[\/latex]. What was the sale price of the sunglasses?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q967734\">Show Answer<\/span><\/p>\n<div id=\"q967734\" class=\"hidden-answer\" style=\"display: none\">\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.\" data-label=\"\">\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=\"The sale price is the original 39 dollar price minus the 10 dollar discount translates to s equals 39 minus 10. The phrase &quot;the sale price&quot; can be represented by s. The word &quot;is&quot; translates to the equals sign. The original 39 dollar price equates to 39. Minus correlates to subtraction. And the 10 dollar discount equates to 10.\" width=\"425\" height=\"76\" data-media-type=\"image\/png\" \/><\/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<\/div>\n<\/div>\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 or static amount. In the next example, the discount is given as a percent of the original price.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/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 the amount of discount and 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 Answer<\/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.\" data-label=\"\">\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=\"The discount is 35 percent of the 140 dollar original price translates to the equation s equals 0.35 times 140. The discount can be represented by s. The word &quot;is&quot; translates to the equals sign. 35 percent becomes 0.35. The word &quot;of&quot; correlates to multiplication. The phrase &quot;the 140 dollar original price&quot; translates to 140.\" width=\"374\" height=\"76\" data-media-type=\"image\/png\" \/><\/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.\" data-label=\"\">\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=\"The sale price is the 140 dollars minus the 49 dollar discount translates to the equation s equals 140 minus 49. The sale price can be represented with s. The word &quot;is&quot; translates to the equals sign. The 140 dollars equates to 140. Minus correlates to subtraction. The 49 dollar discount translates to 49.\" width=\"390\" height=\"76\" data-media-type=\"image\/png\" \/><\/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<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>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 the \u24d0 amount of discount and \u24d1 discount rate.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q123339\">Show Answer<\/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.\" data-label=\"\">\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=\"The discount is the 31 dollar original price minus the 13.95 dollar sale price translates to the equation s equals 31 minus 13.95. The discount can be represented by s. The word &quot;is&quot; translates to the equals sign. The 31 dollar original price equates to 31. Minus correlates to subtraction. The 13.95 dollar sale price equates to 13.95.\" width=\"444\" height=\"76\" data-media-type=\"image\/png\" \/><\/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.\" data-label=\"\">\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 loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3630 size-full\" src=\"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-content\/uploads\/sites\/2985\/2018\/04\/fixed-1.png\" alt=\"The discount of 17.05 dollars is what percent of the 31 dollar original price translates to the equation 17.05 equals r times 31. The discount of 17.05 dollars equates to 17.05. The word &quot;is&quot; translates to the equals sign. What percent can be represented by p. The word &quot;of&quot; correlates to multiplication. The 31 dollar original price equates to 31.\" width=\"221\" height=\"60\" srcset=\"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-content\/uploads\/sites\/2985\/2018\/04\/fixed-1.png 221w, https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-content\/uploads\/sites\/2985\/2018\/04\/fixed-1-65x18.png 65w\" sizes=\"auto, (max-width: 221px) 100vw, 221px\" \/><\/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<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm156971\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=156971&theme=oea&iframe_resize_id=ohm156971&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-1\" 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\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-363\">\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>Screenshot from Big W Square Bedroom Video. <strong>Authored by<\/strong>: Clay Fisher. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/vimeo.com\/266614917\">https:\/\/vimeo.com\/266614917<\/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, Shared previously<\/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":11,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Screenshot from Big W Square Bedroom Video\",\"author\":\"Clay Fisher\",\"organization\":\"\",\"url\":\"https:\/\/vimeo.com\/266614917\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"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\"}]","CANDELA_OUTCOMES_GUID":"09826bf8-3b93-4653-be4c-eefc4507cf46, 09ebc4a8-7e44-405b-924c-66a64b97ed11","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-363","chapter","type-chapter","status-publish","hentry"],"part":26,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/363","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":26,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/363\/revisions"}],"predecessor-version":[{"id":4000,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/363\/revisions\/4000"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/parts\/26"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/363\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/media?parent=363"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapter-type?post=363"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/contributor?post=363"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/license?post=363"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}