{"id":10437,"date":"2017-05-26T20:38:07","date_gmt":"2017-05-26T20:38:07","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10437"},"modified":"2024-04-30T16:42:32","modified_gmt":"2024-04-30T16:42:32","slug":"solving-sales-tax-applications","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/solving-sales-tax-applications\/","title":{"raw":"Solving Sales Tax and Commission Applications","rendered":"Solving Sales Tax and Commission Applications"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Solve sales tax applications<\/li>\r\n \t<li>Solve sales commission applications<\/li>\r\n<\/ul>\r\n<\/div>\r\nSales tax and sales commission are applications of percent in our everyday lives. To solve these types of applications, we will follow the same strategy we used in the section on decimal operations. We show it again here for easy reference.\r\n<div class=\"textbox shaded\">\r\n<h3>Solve an application<\/h3>\r\n<ol id=\"eip-id1168467114891\" class=\"stepwise\">\r\n \t<li>Identify what you are asked to find and choose a variable to represent it.<\/li>\r\n \t<li>Write a sentence that gives the information to find it.<\/li>\r\n \t<li>Translate the sentence into an equation.<\/li>\r\n \t<li>Solve the equation using good algebra techniques.<\/li>\r\n \t<li>Check the answer in the problem and make sure it makes sense.<\/li>\r\n \t<li>Write a complete sentence that answers the question.<\/li>\r\n<\/ol>\r\n<\/div>\r\nRemember that whatever the application, once we write the sentence with the given information (Step 2), we can translate it to a percent equation and then solve it.\r\n<h2>Calculating Sales Tax<\/h2>\r\nDo you pay a tax when you shop in your city or state? In many parts of the United States, sales tax is added to the purchase price of an item (see the image below).\u00a0 The sales tax is determined by computing a percent of the purchase price.\r\n\r\nTo find the sales tax multiply the purchase price by the sales tax rate. Remember to convert the sales tax rate from a percent to a decimal number. Once the sales tax is calculated, it is added to the purchase price. The result is the total cost\u2014this is what the customer pays.\r\n\r\nThe sales tax is calculated as a percent of the purchase price.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222012\/CNX_BMath_Figure_06_03_001.png\" alt=\"A receipt with a list of items including soup, lobster linguini, and other items with a subtotal of $78.25. Tax is 8%. 8% of $78.25 is $6.26 which is added to the subtotal to bring the total to $84.51\" width=\"317\" height=\"475\" \/>\r\n<div class=\"textbox shaded\">\r\n<h3>Sales Tax<\/h3>\r\nThe sales tax is a percent of the purchase price.\r\n\r\n[latex]\\begin{array}{ccc}\\hfill \\text{Sales Tax}&amp; =&amp; \\text{Tax Rate}\\cdot \\text{Purchase Price}\\hfill \\\\ \\hfill \\text{Total Cost}&amp; =&amp; \\text{Purchase Price}+\\text{Sales Tax}\\hfill \\end{array}[\/latex]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nCathy bought a bicycle in Washington, where the sales tax rate was [latex]\\text{6.5%}[\/latex] of the purchase price. What was\r\n\r\n\u24d0 the sales tax and\r\n\u24d1 the total cost of a bicycle if the purchase price of the bicycle was [latex]\\text{\\$392}?[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168469684609\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solve part A. It shows seven steps. Identify what you are asked to find: What is the sales tax? Choose a variable to represent it: Let the variable t be equal to the sales tax. Write a sentence that gives the information to find it: The sales tax is 6.5% of the purchase price. Translate into an equation. Remember to change the percent to a decimal: The sales tax is represented by t. The word 'is' is represented with an equals sign. 6.5% is written as 0.065. The word \">\r\n<tbody>\r\n<tr>\r\n<td>\u24d0<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Identify what you are asked to find.<\/td>\r\n<td>What is the sales tax?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Choose a variable to represent it.<\/td>\r\n<td>Let [latex]t=[\/latex] sales tax.<\/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 sales tax is [latex]6.5\\text{%}[\/latex] of the purchase price.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate into an equation. (Remember to change the percent to a decimal).<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222014\/CNX_BMath_Figure_06_03_014_img-01.png\" alt=\"&quot;The sales tax is 6.5% of the 392 dollars purchase price\u201d can be translated to t equals 0.065 times 392. The parts of the sentence translate as follows: &quot;the sales tax&quot; can be translated to t, the word &quot;is&quot; becomes an equals sign, &quot;6.5%&quot; translates to 0.065, \u201cof\u201d translates to multiplication,  and \u201cthe 392 dollars purchase price\u201d simplifies to 392.\" width=\"407\" height=\"76\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222016\/CNX_BMath_Figure_06_03_014_img-02.png\" alt=\"t equals 25.48\" width=\"407\" height=\"22\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check: Is this answer reasonable?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Yes, because the sales tax amount is less than [latex]10\\text{%}[\/latex] of the purchase 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 sales tax is [latex]\\text{\\$25.48}[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168469712270\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>\u24d1<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Identify what you are asked to find.<\/td>\r\n<td>What is the total cost of the bicycle?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Choose a variable to represent it.<\/td>\r\n<td>Let [latex]c=[\/latex] total cost of bicycle.<\/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 total cost is the purchase price plus the sales tax.<\/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\/24222018\/CNX_BMath_Figure_06_05_014_img-01-01.png\" alt=\"&quot;The total cost is 392 dollars plus 25.48 dollars\u201d can be translated to c equals 392 plus 25.48. The parts of the sentence translate as follows: &quot;the total cost&quot; can be translated to c, the word &quot;is&quot; becomes an equals sign, &quot;392 dollars&quot; translates to 392, \u201cplus\u201d translates to addition,  and \u201c25.48\u201dtranslates to 25.48.\" width=\"407\" height=\"76\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222020\/CNX_BMath_Figure_06_05_014_img-01-02.png\" alt=\"c equals 417.48\" width=\"407\" height=\"22\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check: Is this answer reasonable?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Yes, because the total cost is a little more than the purchase 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 total cost of the bicycle is [latex]\\text{\\$417.48}[\/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]146746[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show an example of how to calculate the sales tax on an item given the tax rate. Note that it does not include calculating the total cost of the item after tax.\r\n\r\nhttps:\/\/youtu.be\/D7B5IzbRS-8\r\n<h2>Calculating Sales Tax Rate<\/h2>\r\nBelow is an example to show how to find the tax rate for an item given the price after tax, and the original price..\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nEvelyn bought a new smartphone for [latex]\\text{\\$499}[\/latex] plus tax. She was surprised when she got the receipt and saw that the tax was [latex]\\text{\\$42.42}[\/latex]. What was the sales tax rate for this purchase?\r\n[reveal-answer q=\"715714\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"715714\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168466580474\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solving the problem. It shows nine steps. Identify what you are asked to find: What is the sales tax rate? Choose a variable you represent it: Let the variable r be equal to the sales tax rate. Write a sentence that gives the information to find it: The sales tax rate is the percent of $499 that is $42.42 tax. Translate into an equation: The percent is represented with the variable r. The word 'of' is represented with a multiplication dot. The price, $499, is written as 499. The word 'is' is represented with an equals sign. The tax, $42.42. is written as 42.42. The equation is r \u00b7 499 = 42.42. Divide: 499 \u00b7 r divided by 499 = 42.42 divided by 499. Simplify: r = 0.085. Change or percent form: r = 8.5%. Write a complete sentence that answers the question: The sales tax rate is 8.5%. Check if this answer is reasonable: Yes, because 8.5% is close to 10%. 10% of $500 is $50, which is close to $42.42.\">\r\n<tbody>\r\n<tr>\r\n<td>Identify what you are asked to find.<\/td>\r\n<td>What is the sales tax 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] sales tax.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence that gives the information to find it.<\/td>\r\n<td>What percent of the price is the sales tax?<\/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\/24222022\/CNX_BMath_Figure_06_03_015_img-01.png\" alt=\"&quot;What percent of 499 dollars is the 42.42 dollars tax?\u201d can be translated to r times 499 equals 42.42. The parts of the sentence translate as follows: &quot;what percent&quot; can be translated to r, the word &quot;of&quot; translates to multiplication, &quot;499 dollars&quot; becomes 499, the word &quot;is&quot; becomes an equals sign, and &quot;the 42.42 dollars tax&quot; simplifies to 42.42.\" width=\"407\" height=\"76\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide.<\/td>\r\n<td>[latex]\\Large\\frac{499r}{499}\\normalsize =\\Large\\frac{42.42}{499}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]r=0.085[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check. Is this answer reasonable?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Yes, because [latex]8.5\\text{%}[\/latex] is close to [latex]10\\text{%}[\/latex].\r\n\r\n[latex]10\\text{%}[\/latex] of [latex]\\text{\\$500}[\/latex] is [latex]\\text{\\$50}[\/latex], which is close to [latex]\\text{\\$42.42}[\/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 sales tax rate is [latex]8.5\\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\u00a0IT<\/h3>\r\n[ohm_question]146750[\/ohm_question]\r\n\r\n<\/div>\r\nWatch this video to see another example of how to find the tax rate for an item given the price after tax, and the original price.\r\n\r\nhttps:\/\/youtu.be\/7cb1lsfU5Rw\r\n<h2>Calculating Original Price<\/h2>\r\nFinally, we see how to calculate the original price given the sales tax rate and the total bill with both the original price plus sales tax as a combined amount.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nEvelyn bought some books at the local bookstore. Her total bill was [latex]$31.50[\/latex], which included \u00a0[latex]5\\%[\/latex] tax. How much did the books cost before tax?\r\n\r\n[reveal-answer q=\"922420\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"922420\"]In this problem, you know that the tax of 5% is added onto the cost of the books. So if the cost of the books is 100%, the cost plus tax is 105%.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}\\text{What number}\\,\\,+5\\%\\,\\,\\text{of that number is}\\,\\,\\$31.50?\\\\105\\%\\,\\,\\text{of what number}=31.50?\\end{array}[\/latex]<\/p>\r\nIdentify the percent, the base, and the amount.\r\n\r\nPercent: [latex]105\\%[\/latex]\r\nBase: [latex]n[\/latex]\r\nAmount: [latex]31.50[\/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}\\\\105\\%\\cdot{n}=31.50\\end{array}[\/latex]<\/p>\r\nConvert [latex]105\\%[\/latex] to a decimal.\r\n<p style=\"text-align: center;\">[latex]1.05\\cdot{n}=31.50[\/latex]<\/p>\r\nDivide to undo the multiplication of <i>n<\/i> times \u00a0[latex]1.05[\/latex].\r\n<p style=\"text-align: center;\">[latex]n=31.50\\div1.05=30[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\nThe books cost [latex]$30[\/latex] before tax.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video example, you will be shown how to find a price before tax using the percent equation.\r\n\r\nhttps:\/\/youtu.be\/qgafD4z8OUE\r\n<h2>Sales Commission<\/h2>\r\nSales people often receive a commission, or percent of total sales, for their sales. Their income may be just the commission they earn, or it may be their commission added to their hourly wages or salary. The commission they earn is calculated as a certain percent of the price of each item they sell. That percent is called the <strong>rate of commission<\/strong>.\r\n<div class=\"textbox shaded\">\r\n<h3>Commission<\/h3>\r\nA commission is a percentage of total sales as determined by the rate of commission.\r\n\r\n[latex]\\text{commission}=\\text{rate of commission}\\cdot \\text{total sales}[\/latex]\r\n\r\n<\/div>\r\nTo find the commission on a sale, multiply the rate of commission by the total sales. Just as we did for computing sales tax, remember to first convert the rate of commission from a percent to a decimal.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nHelene is a realtor. She receives [latex]\\text{3%}[\/latex] commission when she sells a house. How much commission will she receive for selling a house that costs [latex]\\text{\\$260,000}?[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168468246173\" class=\"unnumbered unstyled\" summary=\"The figures shows the steps to solving the problem. It shows eight steps. Identify what you are asked to find: What is the commission? Choose a variable to represent it: Let the variable c be equal the commission. Write a sentence that gives the information to find it: The commission is 3% of the price. Translate into an equation: The commission is represented by c. The word 'is' is represented with an equals sign. 3% is written as 0.03. The word 'of' is represented with a multiplication dot. The price, $260,000, is written as 260,000. The equation is c = 0.03 \u00b7 260,000. Simplify: c = 7,800. Change the commission rate to percent form: r = 8.5%. Write a complete sentence that answers the question: Helene will receive a commission of $7,800. Check if this answer is reasonable: Yes. 1% of $260,000 is $2,600, and $7,800 is three times $2,600.\">\r\n<tbody>\r\n<tr>\r\n<td>Identify what you are asked to find.<\/td>\r\n<td>What is the commission?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Choose a variable to represent it.<\/td>\r\n<td>Let [latex]c=[\/latex] the commission.<\/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 commission is [latex]3\\text{%}[\/latex] of the 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\/24222029\/CNX_BMath_Figure_06_03_016_img-01.png\" alt=\"&quot;The commission is 3% of the 260,000 dollars price.\u201d can be translated to c equals 0.03 times 260000. The parts of the sentence translate as follows: &quot;the commission&quot; can be translated to c, the word &quot;is&quot; beocmes and equals sign, &quot;3%&quot; translates to 0.03, &quot;of&quot; equates to multiplication, and &quot;the 260000 dollars price&quot; simplifies to 260,000. \" width=\"382\" height=\"76\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]c=7800[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check. Is this answer reasonable?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Yes. [latex]1\\text{%}[\/latex] of [latex]\\text{\\$260,000}[\/latex] is [latex]\\text{\\$2,600}[\/latex], and [latex]\\text{\\$7,800}[\/latex] is three times [latex]\\text{\\$2,600}[\/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>Helene will receive a commission of [latex]\\text{\\$7,800}[\/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]146752[\/ohm_question]\r\n\r\n<\/div>\r\nIn this video, we show another example of how to calculate the amount of commission earned given the rate of commission, and the amount of the sale made.\r\n\r\nhttps:\/\/youtu.be\/twARikDLjKg\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nRikki earned [latex]\\text{\\$87}[\/latex] commission when she sold a [latex]\\text{\\$1,450}[\/latex] stove. What rate of commission did she get?\r\n[reveal-answer q=\"175751\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"175751\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468542255\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solving the problem. It shows nine steps. Identify what are asked to find: What is the rate of commission? Choose a variable to represent it: Let the variable r be equal to the rate of commission. Write a sentence that gives the information to find it: The commission is what percent of the sale? Translate into an equation: The commission, $87, is written as 87. 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 amount of the sale, ,450, is written as 1,450. The equation is 87 is equal to r times 1,450. Divide: 87 divided by 1,450 = 1,450 times r divided by 1,450. Simplify: 0.06 is equal to r. Change to percent form: r is equal to 6%. Write a complete sentence that answers the question: The commission was 6% of the price of the stove. Check if this answer is reasonable: Yes. A 10% commission would have been 45. the $6 commission, $87, is a little more than half of that.\">\r\n<tbody>\r\n<tr>\r\n<td>Identify what you are asked to find.<\/td>\r\n<td>What is the rate of commission?<\/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 rate of commission.<\/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 commission is what percent of the sale?<\/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\/24222035\/CNX_BMath_Figure_06_03_017_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide.<\/td>\r\n<td>[latex]\\Large\\frac{87}{1450}\\normalsize =\\Large\\frac{1450r}{1450}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]0.06=r[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change to percent form.<\/td>\r\n<td>[latex]r=6\\text{%}[\/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]10\\text{%}[\/latex] commission would have been [latex]\\text{\\$145}[\/latex].\r\n\r\nThe [latex]6\\text{%}[\/latex] commission, [latex]\\text{\\$87}[\/latex], is a little more than half of that.<\/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 commission was [latex]6\\text{%}[\/latex] of the price of the stove.<\/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]146754[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Solve sales tax applications<\/li>\n<li>Solve sales commission applications<\/li>\n<\/ul>\n<\/div>\n<p>Sales tax and sales commission are applications of percent in our everyday lives. To solve these types of applications, we will follow the same strategy we used in the section on decimal operations. We show it again here for easy reference.<\/p>\n<div class=\"textbox shaded\">\n<h3>Solve an application<\/h3>\n<ol id=\"eip-id1168467114891\" class=\"stepwise\">\n<li>Identify what you are asked to find and choose a variable to represent it.<\/li>\n<li>Write a sentence that gives the information to find it.<\/li>\n<li>Translate the sentence into an equation.<\/li>\n<li>Solve the equation using good algebra techniques.<\/li>\n<li>Check the answer in the problem and make sure it makes sense.<\/li>\n<li>Write a complete sentence that answers the question.<\/li>\n<\/ol>\n<\/div>\n<p>Remember that whatever the application, once we write the sentence with the given information (Step 2), we can translate it to a percent equation and then solve it.<\/p>\n<h2>Calculating Sales Tax<\/h2>\n<p>Do you pay a tax when you shop in your city or state? In many parts of the United States, sales tax is added to the purchase price of an item (see the image below).\u00a0 The sales tax is determined by computing a percent of the purchase price.<\/p>\n<p>To find the sales tax multiply the purchase price by the sales tax rate. Remember to convert the sales tax rate from a percent to a decimal number. Once the sales tax is calculated, it is added to the purchase price. The result is the total cost\u2014this is what the customer pays.<\/p>\n<p>The sales tax is calculated as a percent of the purchase price.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222012\/CNX_BMath_Figure_06_03_001.png\" alt=\"A receipt with a list of items including soup, lobster linguini, and other items with a subtotal of $78.25. Tax is 8%. 8% of $78.25 is $6.26 which is added to the subtotal to bring the total to $84.51\" width=\"317\" height=\"475\" \/><\/p>\n<div class=\"textbox shaded\">\n<h3>Sales Tax<\/h3>\n<p>The sales tax is a percent of the purchase price.<\/p>\n<p>[latex]\\begin{array}{ccc}\\hfill \\text{Sales Tax}& =& \\text{Tax Rate}\\cdot \\text{Purchase Price}\\hfill \\\\ \\hfill \\text{Total Cost}& =& \\text{Purchase Price}+\\text{Sales Tax}\\hfill \\end{array}[\/latex]<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Cathy bought a bicycle in Washington, where the sales tax rate was [latex]\\text{6.5%}[\/latex] of the purchase price. What was<\/p>\n<p>\u24d0 the sales tax and<br \/>\n\u24d1 the total cost of a bicycle if the purchase price of the bicycle was [latex]\\text{\\$392}?[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168469684609\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solve part A. It shows seven steps. Identify what you are asked to find: What is the sales tax? Choose a variable to represent it: Let the variable t be equal to the sales tax. Write a sentence that gives the information to find it: The sales tax is 6.5% of the purchase price. Translate into an equation. Remember to change the percent to a decimal: The sales tax is represented by t. The word 'is' is represented with an equals sign. 6.5% is written as 0.065. The word\">\n<tbody>\n<tr>\n<td>\u24d0<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>What is the sales tax?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]t=[\/latex] sales tax.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>The sales tax is [latex]6.5\\text{%}[\/latex] of the purchase price.<\/td>\n<\/tr>\n<tr>\n<td>Translate into an equation. (Remember to change the percent to a decimal).<\/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\/24222014\/CNX_BMath_Figure_06_03_014_img-01.png\" alt=\"&quot;The sales tax is 6.5% of the 392 dollars purchase price\u201d can be translated to t equals 0.065 times 392. The parts of the sentence translate as follows: &quot;the sales tax&quot; can be translated to t, the word &quot;is&quot; becomes an equals sign, &quot;6.5%&quot; translates to 0.065, \u201cof\u201d translates to multiplication,  and \u201cthe 392 dollars purchase price\u201d simplifies to 392.\" width=\"407\" height=\"76\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/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\/24222016\/CNX_BMath_Figure_06_03_014_img-02.png\" alt=\"t equals 25.48\" width=\"407\" height=\"22\" \/><\/td>\n<\/tr>\n<tr>\n<td>Check: Is this answer reasonable?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes, because the sales tax amount is less than [latex]10\\text{%}[\/latex] of the purchase price.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The sales tax is [latex]\\text{\\$25.48}[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469712270\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>\u24d1<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>What is the total cost of the bicycle?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]c=[\/latex] total cost of bicycle.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>The total cost is the purchase price plus the sales tax.<\/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\/24222018\/CNX_BMath_Figure_06_05_014_img-01-01.png\" alt=\"&quot;The total cost is 392 dollars plus 25.48 dollars\u201d can be translated to c equals 392 plus 25.48. The parts of the sentence translate as follows: &quot;the total cost&quot; can be translated to c, the word &quot;is&quot; becomes an equals sign, &quot;392 dollars&quot; translates to 392, \u201cplus\u201d translates to addition,  and \u201c25.48\u201dtranslates to 25.48.\" width=\"407\" height=\"76\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/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\/24222020\/CNX_BMath_Figure_06_05_014_img-01-02.png\" alt=\"c equals 417.48\" width=\"407\" height=\"22\" \/><\/td>\n<\/tr>\n<tr>\n<td>Check: Is this answer reasonable?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes, because the total cost is a little more than the purchase price.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The total cost of the bicycle is [latex]\\text{\\$417.48}[\/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=\"ohm146746\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146746&theme=oea&iframe_resize_id=ohm146746&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show an example of how to calculate the sales tax on an item given the tax rate. Note that it does not include calculating the total cost of the item after tax.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex: Percent Application - Sales Tax Given Percent (Equation and Proportion)\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/D7B5IzbRS-8?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Calculating Sales Tax Rate<\/h2>\n<p>Below is an example to show how to find the tax rate for an item given the price after tax, and the original price..<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Evelyn bought a new smartphone for [latex]\\text{\\$499}[\/latex] plus tax. She was surprised when she got the receipt and saw that the tax was [latex]\\text{\\$42.42}[\/latex]. What was the sales tax rate for this purchase?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q715714\">Show Solution<\/span><\/p>\n<div id=\"q715714\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168466580474\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solving the problem. It shows nine steps. Identify what you are asked to find: What is the sales tax rate? Choose a variable you represent it: Let the variable r be equal to the sales tax rate. Write a sentence that gives the information to find it: The sales tax rate is the percent of $499 that is $42.42 tax. Translate into an equation: The percent is represented with the variable r. The word 'of' is represented with a multiplication dot. The price, $499, is written as 499. The word 'is' is represented with an equals sign. The tax, $42.42. is written as 42.42. The equation is r \u00b7 499 = 42.42. Divide: 499 \u00b7 r divided by 499 = 42.42 divided by 499. Simplify: r = 0.085. Change or percent form: r = 8.5%. Write a complete sentence that answers the question: The sales tax rate is 8.5%. Check if this answer is reasonable: Yes, because 8.5% is close to 10%. 10% of $500 is $50, which is close to $42.42.\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>What is the sales tax rate?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]r=[\/latex] sales tax.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>What percent of the price is the sales tax?<\/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\/24222022\/CNX_BMath_Figure_06_03_015_img-01.png\" alt=\"&quot;What percent of 499 dollars is the 42.42 dollars tax?\u201d can be translated to r times 499 equals 42.42. The parts of the sentence translate as follows: &quot;what percent&quot; can be translated to r, the word &quot;of&quot; translates to multiplication, &quot;499 dollars&quot; becomes 499, the word &quot;is&quot; becomes an equals sign, and &quot;the 42.42 dollars tax&quot; simplifies to 42.42.\" width=\"407\" height=\"76\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td>[latex]\\Large\\frac{499r}{499}\\normalsize =\\Large\\frac{42.42}{499}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]r=0.085[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check. Is this answer reasonable?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes, because [latex]8.5\\text{%}[\/latex] is close to [latex]10\\text{%}[\/latex].<\/p>\n<p>[latex]10\\text{%}[\/latex] of [latex]\\text{\\$500}[\/latex] is [latex]\\text{\\$50}[\/latex], which is close to [latex]\\text{\\$42.42}[\/latex].<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The sales tax rate is [latex]8.5\\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\u00a0IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146750\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146750&theme=oea&iframe_resize_id=ohm146750&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch this video to see another example of how to find the tax rate for an item given the price after tax, and the original price.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex: Find the Sale Tax Percentage\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/7cb1lsfU5Rw?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Calculating Original Price<\/h2>\n<p>Finally, we see how to calculate the original price given the sales tax rate and the total bill with both the original price plus sales tax as a combined amount.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Evelyn bought some books at the local bookstore. Her total bill was [latex]$31.50[\/latex], which included \u00a0[latex]5\\%[\/latex] tax. How much did the books cost before tax?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q922420\">Show Solution<\/span><\/p>\n<div id=\"q922420\" class=\"hidden-answer\" style=\"display: none\">In this problem, you know that the tax of 5% is added onto the cost of the books. So if the cost of the books is 100%, the cost plus tax is 105%.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}\\text{What number}\\,\\,+5\\%\\,\\,\\text{of that number is}\\,\\,\\$31.50?\\\\105\\%\\,\\,\\text{of what number}=31.50?\\end{array}[\/latex]<\/p>\n<p>Identify the percent, the base, and the amount.<\/p>\n<p>Percent: [latex]105\\%[\/latex]<br \/>\nBase: [latex]n[\/latex]<br \/>\nAmount: [latex]31.50[\/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}\\\\105\\%\\cdot{n}=31.50\\end{array}[\/latex]<\/p>\n<p>Convert [latex]105\\%[\/latex] to a decimal.<\/p>\n<p style=\"text-align: center;\">[latex]1.05\\cdot{n}=31.50[\/latex]<\/p>\n<p>Divide to undo the multiplication of <i>n<\/i> times \u00a0[latex]1.05[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]n=31.50\\div1.05=30[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>The books cost [latex]$30[\/latex] before tax.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the following video example, you will be shown how to find a price before tax using the percent equation.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Percent App:  Find a Price Before Tax From Total Price\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/qgafD4z8OUE?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Sales Commission<\/h2>\n<p>Sales people often receive a commission, or percent of total sales, for their sales. Their income may be just the commission they earn, or it may be their commission added to their hourly wages or salary. The commission they earn is calculated as a certain percent of the price of each item they sell. That percent is called the <strong>rate of commission<\/strong>.<\/p>\n<div class=\"textbox shaded\">\n<h3>Commission<\/h3>\n<p>A commission is a percentage of total sales as determined by the rate of commission.<\/p>\n<p>[latex]\\text{commission}=\\text{rate of commission}\\cdot \\text{total sales}[\/latex]<\/p>\n<\/div>\n<p>To find the commission on a sale, multiply the rate of commission by the total sales. Just as we did for computing sales tax, remember to first convert the rate of commission from a percent to a decimal.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Helene is a realtor. She receives [latex]\\text{3%}[\/latex] commission when she sells a house. How much commission will she receive for selling a house that costs [latex]\\text{\\$260,000}?[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168468246173\" class=\"unnumbered unstyled\" summary=\"The figures shows the steps to solving the problem. It shows eight steps. Identify what you are asked to find: What is the commission? Choose a variable to represent it: Let the variable c be equal the commission. Write a sentence that gives the information to find it: The commission is 3% of the price. Translate into an equation: The commission is represented by c. The word 'is' is represented with an equals sign. 3% is written as 0.03. The word 'of' is represented with a multiplication dot. The price, $260,000, is written as 260,000. The equation is c = 0.03 \u00b7 260,000. Simplify: c = 7,800. Change the commission rate to percent form: r = 8.5%. Write a complete sentence that answers the question: Helene will receive a commission of $7,800. Check if this answer is reasonable: Yes. 1% of $260,000 is $2,600, and $7,800 is three times $2,600.\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>What is the commission?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]c=[\/latex] the commission.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>The commission is [latex]3\\text{%}[\/latex] of the 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\/24222029\/CNX_BMath_Figure_06_03_016_img-01.png\" alt=\"&quot;The commission is 3% of the 260,000 dollars price.\u201d can be translated to c equals 0.03 times 260000. The parts of the sentence translate as follows: &quot;the commission&quot; can be translated to c, the word &quot;is&quot; beocmes and equals sign, &quot;3%&quot; translates to 0.03, &quot;of&quot; equates to multiplication, and &quot;the 260000 dollars price&quot; simplifies to 260,000.\" width=\"382\" height=\"76\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]c=7800[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check. Is this answer reasonable?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. [latex]1\\text{%}[\/latex] of [latex]\\text{\\$260,000}[\/latex] is [latex]\\text{\\$2,600}[\/latex], and [latex]\\text{\\$7,800}[\/latex] is three times [latex]\\text{\\$2,600}[\/latex].<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>Helene will receive a commission of [latex]\\text{\\$7,800}[\/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=\"ohm146752\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146752&theme=oea&iframe_resize_id=ohm146752&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In this video, we show another example of how to calculate the amount of commission earned given the rate of commission, and the amount of the sale made.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Ex: Percent Application - Commission Amount Given Percent of Sales (Equation and Proportion)\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/twARikDLjKg?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Rikki earned [latex]\\text{\\$87}[\/latex] commission when she sold a [latex]\\text{\\$1,450}[\/latex] stove. What rate of commission did she get?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q175751\">Show Solution<\/span><\/p>\n<div id=\"q175751\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468542255\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solving the problem. It shows nine steps. Identify what are asked to find: What is the rate of commission? Choose a variable to represent it: Let the variable r be equal to the rate of commission. Write a sentence that gives the information to find it: The commission is what percent of the sale? Translate into an equation: The commission, $87, is written as 87. 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 amount of the sale, ,450, is written as 1,450. The equation is 87 is equal to r times 1,450. Divide: 87 divided by 1,450 = 1,450 times r divided by 1,450. Simplify: 0.06 is equal to r. Change to percent form: r is equal to 6%. Write a complete sentence that answers the question: The commission was 6% of the price of the stove. Check if this answer is reasonable: Yes. A 10% commission would have been 45. the $6 commission, $87, is a little more than half of that.\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>What is the rate of commission?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]r=[\/latex] the rate of commission.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>The commission is what percent of the sale?<\/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\/24222035\/CNX_BMath_Figure_06_03_017_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td>[latex]\\Large\\frac{87}{1450}\\normalsize =\\Large\\frac{1450r}{1450}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]0.06=r[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change to percent form.<\/td>\n<td>[latex]r=6\\text{%}[\/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]10\\text{%}[\/latex] commission would have been [latex]\\text{\\$145}[\/latex].<\/p>\n<p>The [latex]6\\text{%}[\/latex] commission, [latex]\\text{\\$87}[\/latex], is a little more than half of that.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>The commission was [latex]6\\text{%}[\/latex] of the price of the stove.<\/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=\"ohm146754\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146754&theme=oea&iframe_resize_id=ohm146754&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-10437\">\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 146746, 146750. <strong>Authored by<\/strong>: LumenLearning. <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>Ex: Find the Sale Tax Percentage. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/7cb1lsfU5Rw\">https:\/\/youtu.be\/7cb1lsfU5Rw<\/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>Ex: Percent Application - Sales Tax Given Percent (Equation and Proportion). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/D7B5IzbRS-8\">https:\/\/youtu.be\/D7B5IzbRS-8<\/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":14,"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 146746, 146750\",\"author\":\"LumenLearning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Find the Sale Tax Percentage\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/7cb1lsfU5Rw\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Percent Application - 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