{"id":6993,"date":"2020-11-03T16:00:12","date_gmt":"2020-11-03T16:00:12","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/slcc-beginalgebra\/?post_type=chapter&#038;p=6993"},"modified":"2026-01-12T21:20:41","modified_gmt":"2026-01-12T21:20:41","slug":"1-8-applications-involving-percent","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-elementaryalgebra\/chapter\/1-8-applications-involving-percent\/","title":{"raw":"1.8: Applications Involving Percent","rendered":"1.8: Applications Involving Percent"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>SECTION 1.8 Learning Objectives<\/h3>\r\n<strong>1.8: Applications Involving Percent<\/strong>\r\n<ul>\r\n \t<li>Use an algebraic equation to solve a basic percent question<\/li>\r\n \t<li>Use an algebraic equation to solve application problems involving percent<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Percent of a Whole<\/h2>\r\nPercents are the ratio of a number and 100. Percents are used in many different applications. Percents are used widely to describe how something changed. For example, you may have heard that the amount of rainfall this month had decreased by 12% from last year, or that the number of jobless claims has increase by 5% this quarter over last quarter.\r\n\r\n[caption id=\"attachment_3014\" align=\"aligncenter\" width=\"300\"]<img class=\"wp-image-3014 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/117\/2016\/04\/20194605\/Screen-Shot-2016-04-20-at-12.44.43-PM-300x209.png\" alt=\"A graph showing the seasonally adjusted unemployment rate, with the y-axis representing percent from 4 to 10 and the x-axis representing time in years.\" width=\"300\" height=\"209\" \/> Unemployment rate as percent by year between 2004 and 2014.[\/caption]\r\n\r\nWe regularly use this kind of language to quickly describe how much something increased or decreased over time or between significant events.\r\n\r\nBefore we dissect the methods for finding percent change of a quantity, let's learn the basics of finding percent of a whole.\r\n\r\nFor example, if we knew a gas tank held 14 gallons, and wanted to know how many gallons were in [latex]\\frac{1}{4}[\/latex]\u00a0of a tank, we would find [latex]\\frac{1}{4}[\/latex]\u00a0of 14 gallons by multiplying:\r\n<p style=\"text-align: center;\">[latex] \\frac{1}{4}\\,\\cdot \\,14=\\frac{1}{4}\\,\\cdot \\,\\frac{14}{1}=\\frac{14}{4}=3\\frac{2}{4}=3\\frac{1}{2}\\,\\,\\,\\text{gallons}[\/latex]<\/p>\r\nLikewise, if we wanted to find 25% of 14 gallons, we could find this by multiplying, but first we would need to convert the 25% to a decimal:\r\n<p style=\"text-align: center;\">[latex]25\\%\\,\\,\\text{of}\\,\\,14\\,\\,\\,\\text{gallons}=0.25\\,\\cdot \\,14=3.5\\,\\,\\,\\text{gallons}[\/latex]<\/p>\r\n&nbsp;\r\n<div class=\"textbox shaded\">\r\n<h3>Finding a Percent of a Whole<\/h3>\r\nTo find a percent of a whole,\r\n<ul>\r\n \t<li>Write the percent as a decimal by moving the decimal two places to the left<\/li>\r\n \t<li>Then multiply the percent by the whole amount<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example 1<\/h3>\r\nWhat is 10% of $200?\r\n\r\n[reveal-answer q=\"834578\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"834578\"]Write as a decimal.\u00a0Move the decimal point two places to the left.\r\n<p style=\"text-align: center;\">[latex]10\\%=0.10[\/latex]<\/p>\r\nMultiply the decimal form of the percent by the whole number.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}0.10\\cdot200\\\\20\\end{array}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n10% of $200 is $20.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNotice in the example above that 10% of 200 is 20. Finding 10% of a number is one of the easiest percentages to calculate.\u00a0To calculate\u00a0<b>10 percent of a number<\/b>, we always simply divide it by\u00a0<b>10<\/b>\u00a0or <strong>move the decimal point one place to the left.<\/strong>\u00a0 For example, 10% of 325 is 32.5.\u00a0 Being able to recall what 10% of a value is might often be helpful when reflecting on the reasonableness of your answers to problems involving different percentages as you will see in some examples in this section.\r\n\r\nThe following video contains an example that is similar to the one above.\r\n\r\nhttps:\/\/youtu.be\/jTM7ZMvAzsc\r\n\r\n&nbsp;\r\n<h2>Use an algebraic equation to solve a basic percent question<\/h2>\r\nFrom the previous examples, we can identify\u00a0some important parts to finding the percent of a whole. We are going to focus on the equation method to solve problems involving percent.\u00a0 To translate the following problems into equations, we need to know a few key words and what they mean.\r\n<ul>\r\n \t<li><strong>\u201cof\u201d<\/strong> means multiply<\/li>\r\n \t<li><strong>\u201cis\u201d<\/strong> means equals<\/li>\r\n \t<li><strong>\u201cwhat\u201d<\/strong> can be represented by the variable<\/li>\r\n<\/ul>\r\nThe following examples show how to use an algebraic equation to solve a basic percent question:\r\n<div class=\"textbox exercises\">\r\n<h3>Example 2<\/h3>\r\nWhat is 12% of 270?\r\n\r\n[reveal-answer q=\"791982\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"791982\"]\r\n\r\nIn this question, we will replace:\r\n\r\n<span style=\"color: #ff0000;\"><strong>\u201cwhat\u201d<\/strong><\/span> with the variable [latex]x[\/latex],\r\n\r\n<span style=\"color: #008000;\"><strong>\u201cis\u201d<\/strong><\/span> with the equals sign,\r\n\r\n<span style=\"color: #0000ff;\"><strong>\u201cof\u201d<\/strong><\/span> with the multiplication symbol.\r\n\r\nWe also need to convert the percentage into a decimal number before writing it in our equation.\u00a0 To convert a percentage to a decimal number, we move the decimal two places to the left.\u00a0 Why is it two places?\u00a0 Percent means \u201cper hundred.\u201d\u00a0 Therefore, 12% means 12\/100.\u00a0 Dividing 12 by 100 gives the result of 0.12.\u00a0 Since we will always be dividing by 100 to convert percentages to decimal numbers, we will always move the decimal two places to the left.\r\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">What<\/span> <span style=\"color: #008000;\">is<\/span><\/strong> 12% <strong><span style=\"color: #0000ff;\">of<\/span><\/strong> 270?<\/p>\r\n<p style=\"text-align: center;\">[latex]{\\color{red}x}\\hspace{.04in} {\\mathbf{\\color{green}=}}\\hspace{.04in}0.12\\hspace{.03in}\\vcenter{\\hbox{$\\scriptscriptstyle \\color{blue} \\bullet$}}\\hspace{.03in}270[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]x=32.4[\/latex]<\/p>\r\n<p style=\"text-align: center;\">32.4 is 12% of 270<\/p>\r\n*Reflect on your answer and make sure it is reasonable! We can recall that 10% of 270 would be 27.0, so since 12% is just a slightly larger percentage than 10%, it makes sense that 32.5 (which is slightly bigger than 27) is 12% of the number 270.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example 3<\/h3>\r\n30 is 20% of what number?\r\n\r\n[reveal-answer q=\"204160\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"204160\"]\r\n\r\nIn this question, we will replace:\r\n\r\n<span style=\"color: #ff0000;\"><strong>\u201cwhat number\u201d<\/strong><\/span> with the variable [latex]x[\/latex],\r\n\r\n<span style=\"color: #008000;\"><strong>\u201cis\u201d<\/strong><\/span> with the equals sign,\r\n\r\n<span style=\"color: #0000ff;\"><strong>\u201cof\u201d<\/strong><\/span> with the multiplication symbol.\r\n<p style=\"text-align: center;\">30 <span style=\"color: #008000;\"><strong>is<\/strong><\/span> 20% <span style=\"color: #0000ff;\"><strong>of<\/strong><\/span> <span style=\"color: #ff0000;\"><strong>what number?<\/strong><\/span><\/p>\r\n<p style=\"text-align: center;\">[latex]30\\hspace{.04in}{\\mathbf{\\color{green} =}}\\hspace{.04in}0.20\\hspace{.03in}\\vcenter{\\hbox{$\\scriptscriptstyle \\color{blue} \\bullet$}}\\hspace{.03in}{\\color{red} x}[\/latex]<\/p>\r\n<p style=\"text-align: left;\">Solve for x by dividing by both sides by 0.20<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{30}{0.20}=\\frac{0.20\\cdot x}{0.20}[\/latex]<\/p>\r\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">[latex]150=x[\/latex]<\/span><\/p>\r\n\r\n<h4>Answer<\/h4>\r\n30 is 20% of 150.\r\n\r\n*Reflect on your answer to see if it is reasonable! The problem stated that 30 is 20% of some number. If 30 is a percentage of a number, that means it is a portion of the whole. The number we are finding must be <em>larger than<\/em> 30. We can recall that 30 is 10% of 300. It makes sense then that is 30 equates to 20% of 150.\u00a0 Our answer of 150 is reasonable. 30 is 20% of 150.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe previous problem states that 30 is a portion of another number.\u00a0 Note that this problem could be rewritten: 20% of what number is 30?\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example 4<\/h3>\r\nWhat percent of 72 is 9?\r\n\r\n[reveal-answer q=\"850317\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"850317\"]\r\n\r\nIn this question, we will replace:\r\n\r\n<span style=\"color: #ff0000;\"><strong>\u201cwhat percent\u201d<\/strong><\/span> with the variable [latex]x[\/latex],\r\n\r\n<span style=\"color: #008000;\"><strong>\u201cis\u201d<\/strong><\/span> with the equals sign,\r\n\r\n<span style=\"color: #0000ff;\"><strong>\u201cof\u201d<\/strong><\/span> with the multiplication symbol.\r\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">What percent<\/span> <span style=\"color: #0000ff;\">of<\/span><\/strong> 72 <strong><span style=\"color: #008000;\">is<\/span><\/strong> 9?<\/p>\r\n<p style=\"text-align: center;\">[latex]{\\color{red}x}\\hspace{.03in}\\vcenter{\\hbox{$\\scriptscriptstyle \\color{blue} \\bullet$}}\\hspace{.03in}72\\hspace{.04in}{\\mathbf{\\color{green}=}}\\hspace{.04in}9[\/latex]<\/p>\r\nDivide to undo the multiplication of x times 72.\r\n<p style=\"text-align: center;\">[latex]\\frac{x\\cdot 72}{72}=\\frac{9}{72}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]x=\\frac{9}{72}[\/latex]<\/p>\r\nDivide 9 by 72 to find the value for x, the unknown.\r\n<p style=\"text-align: center;\">[latex]x=0.125[\/latex]<\/p>\r\nSince we are looking for a percent, we need to convert the decimal answer we got for x into a percentage. We do that by moving the decimal two places to the right. In order to convert a decimal to a percent, we multiply by 100. Multiplying by 100 always moves the decimal two places to the right.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}x=0.125\\\\x=12.5\\%\\end{array}[\/latex]<\/p>\r\n&nbsp;\r\n<h4>Answer<\/h4>\r\n12.5% of 72 is 9.\r\n\r\n*Reflect on your answer to see if it is reasonable! From what is given, we know that 9 is a portion of 72. Use 10% to see if it gets you close to the answer. We might recall that 7.2 is 10% of 72 so it makes sense that 9 (which is slightly larger that 7.2) would be a slightly larger percentage of 72, at 12.5%. Our answer makes sense!\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nBelow are some additional video examples to view:\r\n\r\nhttps:\/\/youtu.be\/A_IHTwXWXl0\r\n\r\nhttps:\/\/youtu.be\/ke4ZTaI1wt8\r\n\r\nhttps:\/\/youtu.be\/3x4K9zggNt8\r\n\r\nTry some of the examples on your own before revealing the answer.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example 5<\/h3>\r\nWhat is 110% of 24?\r\n\r\n[reveal-answer q=\"108201\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"108201\"]\r\n\r\nIn this question, we will replace:\r\n\r\n<span style=\"color: #ff0000;\"><strong>\u201cwhat\u201d<\/strong><\/span> with the variable [latex]x[\/latex],\r\n\r\n<span style=\"color: #008000;\"><strong>\u201cis\u201d<\/strong><\/span> with the equals sign,\r\n\r\n<span style=\"color: #0000ff;\"><strong>\u201cof\u201d<\/strong><\/span> with the multiplication symbol.\r\n<p style=\"text-align: center;\"><span style=\"color: #ff0000;\"><strong>What<\/strong><\/span> <strong><span style=\"color: #008000;\">is<\/span> <\/strong>110% <strong><span style=\"color: #0000ff;\">of<\/span><\/strong> 24?<\/p>\r\n<p style=\"text-align: center;\">[latex]{\\color{red}x}\\hspace{.04in}{\\mathbf{\\color{green}=}}\\hspace{.04in}1.10\\hspace{.03in}\\vcenter{\\hbox{$\\scriptscriptstyle \\color{blue} \\bullet$}}\\hspace{.03in}24[\/latex]<\/p>\r\nWrite the percent as a decimal by moving the decimal point two places to the left.\r\n\r\n&nbsp;\r\n<p style=\"text-align: center;\">[latex]x = 1.10 \\cdot 24[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]x = 1.10 \\cdot 24[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]x = 26.4[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n26.4 is 110% of 24.\r\n\r\n* Reflect on your answer to see if it is reasonable! This problem is a little easier to estimate. 100% of 24 is 24. And 110% is a little bit more than 24. So, 26.4 is a reasonable answer.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example 6<\/h3>\r\nWhat percent of 70.52 is 13.27?\u00a0 Round answer to the nearest tenth of a percent.\r\n\r\n[reveal-answer q=\"272806\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"272806\"]\r\n\r\nIn this question, we will replace:\r\n\r\n<span style=\"color: #ff0000;\"><strong>\u201cwhat percent\u201d<\/strong><\/span> with the variable [latex]x[\/latex],\r\n\r\n<span style=\"color: #008000;\"><strong>\u201cis\u201d<\/strong><\/span> with the equals sign,\r\n\r\n<span style=\"color: #0000ff;\"><strong>\u201cof\u201d<\/strong><\/span> with the multiplication symbol.\r\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">What percent<\/span> <span style=\"color: #0000ff;\">of<\/span> <\/strong>70.52 <strong><span style=\"color: #008000;\">is<\/span><\/strong> 13.27?<\/p>\r\n<p style=\"text-align: center;\">[latex] {\\color{red}x}\\hspace{.03in}\\vcenter{\\hbox{$\\scriptscriptstyle \\color{blue} \\bullet$}}\\hspace{.03in}70.52 \\hspace{.04in}{\\mathbf{\\color{green}=}}\\hspace{.04in}13.27[\/latex]<\/p>\r\nDivide to undo the multiplication of x times 70.52.\r\n<p style=\"text-align: center;\">[latex]\\frac{x\\cdot 70.52}{70.52}=\\frac{13.27}{70.52}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]x=\\frac{13.27}{70.52}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]x=0.1881735...[\/latex]<\/p>\r\nSince we are trying to find \"what percent\", convert our answer to a percentage BEFORE rounding.\u00a0 We do that by moving the decimal two places to the right.\u00a0 In order to convert a decimal to a percent, we multiply by 100.\u00a0 Multiplying by 100 always moves the decimal two places to the right.\r\n<p style=\"text-align: center;\">[latex]x=18.81735..\\%[\/latex]<\/p>\r\nRound to the nearest tenth of a percent\r\n<p style=\"text-align: center;\">[latex]x=18.8\\%[\/latex]<\/p>\r\n&nbsp;\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div><\/div>\r\n<h2 class=\"textbox shaded\"><strong>Note:<\/strong> Often times, problems like the ones in this section will ask you to round your final answer. If you need a review on rounding, refer back to Module 0 of this textbook:\u00a0 <a href=\"https:\/\/courses.lumenlearning.com\/slcc-elementaryalgebra\/chapter\/rounding-decimals\/\">Module 0: Rounding Decimals Review<\/a><\/h2>\r\n<h2>Use an algebraic equation to solve application problems involving percent<\/h2>\r\nPercents have a wide variety of applications to everyday life, showing up regularly in taxes, discounts, markups, and interest rates. We will look at several examples of how to use percent to calculate markups, discounts, and interest earned or owed.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example 7<\/h3>\r\nJeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off of the $220 original price<i>.<\/i>\r\n\r\n[reveal-answer q=\"285084\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"285084\"]First, we need to identify what it is we are being asked to find.\u00a0 We can summarize the problem with the question,\r\n<p style=\"text-align: center;\">What is 15% of $220?<\/p>\r\nOnce we identify that question, we can translate it into an equation.\r\n\r\nIn this question, we will replace:\r\n\r\n<span style=\"color: #ff0000;\"><strong>\u201cwhat\u201d<\/strong><\/span> with the variable [latex]x[\/latex],\r\n\r\n<span style=\"color: #008000;\"><strong>\u201cis\u201d<\/strong><\/span> with the equals sign,\r\n\r\n<span style=\"color: #0000ff;\"><strong>\u201cof\u201d<\/strong><\/span> with the multiplication symbol.\r\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">What<\/span> <span style=\"color: #008000;\">is<\/span><\/strong> 15% <strong><span style=\"color: #0000ff;\">of<\/span> <\/strong>$220?<\/p>\r\n<p style=\"text-align: center;\">[latex]{\\color{red}x}\\hspace{.04in}{\\mathbf{\\color{green}=}}\\hspace{.04in}15\\hbox{%}\\hspace{.03in}\\vcenter{\\hbox{$\\scriptscriptstyle \\color{blue} \\bullet$}}\\hspace{.03in}220[\/latex]<\/p>\r\nConvert 15% to 0.15, then multiply by 220.\r\n<p style=\"text-align: center;\">[latex]x= 0.15\\cdot220=33[\/latex]<\/p>\r\nSo, 15% of $220 is $33.\r\n<h4>Answer<\/h4>\r\nThe coupon will take $33 off the original price.\r\n*You can estimate to see if the answer is reasonable. Since 15% is half way between 10% and 20%, 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, 33, is between 22 and 44. So $33 seems reasonable.\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example 8<\/h3>\r\nTracey paid $185 for an item that was originally priced at $390.\u00a0 What percent of the original price did Tracey pay?\u00a0 Round answer to the nearest tenth of a percent.\r\n\r\n[reveal-answer q=\"30765\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"30765\"]\u00a0We can summarize the problem with the question,\r\n<p style=\"text-align: center;\">What percent of $390 is $185?<\/p>\r\nOnce we identify that question, we can translate it into an equation.\r\n\r\nIn this question, we will replace:\r\n\r\n<span style=\"color: #ff0000;\"><strong>\u201cwhat percent\u201d<\/strong><\/span> with the variable [latex]x[\/latex],\r\n\r\n<span style=\"color: #008000;\"><strong>\u201cis\u201d<\/strong><\/span> with the equals sign,\r\n\r\n<span style=\"color: #0000ff;\"><strong>\u201cof\u201d<\/strong><\/span> with the multiplication symbol.\r\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">What percent<\/span> <span style=\"color: #0000ff;\">of<\/span> <\/strong>$390 <strong><span style=\"color: #008000;\">is<\/span><\/strong> $185?<\/p>\r\n<p style=\"text-align: center;\">[latex]{\\color{red}x}\\hspace{.03in}\\vcenter{\\hbox{$\\scriptscriptstyle \\color{blue} \\bullet$}}\\hspace{.03in}390\\hspace{.04in}{\\mathbf{\\color{green}=}} 185[\/latex]<\/p>\r\nDivide to undo the multiplication of x times 390.\r\n<p style=\"text-align: center;\">[latex]\\frac{x\\cdot 390}{390}=\\frac{185}{390}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]x=\\frac{185}{390}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]x=0.474358974...[\/latex]<\/p>\r\nSince we are looking for a percent, we still need to convert this decimal answer into a percent.\u00a0 Remember we do that by moving the decimal two places to the right.\r\n<p style=\"text-align: center;\">[latex]x=47.4358974..\\%[\/latex]<\/p>\r\nRound to the nearest tenth of a percent\r\n<p style=\"text-align: center;\">[latex]x=47.4\\%[\/latex]<\/p>\r\nTracey paid 47.4% of the original price.\r\n\r\n*Reflect if your answer is reasonable! We can find 50% fairly easily by dividing $390 by 2. We see that $195 is 50% of $390, so it makes sense that $185 (which is a little less than $195), is about 47.4% of $390 (which is a little less than 50%).\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;","rendered":"<div class=\"textbox learning-objectives\">\n<h3>SECTION 1.8 Learning Objectives<\/h3>\n<p><strong>1.8: Applications Involving Percent<\/strong><\/p>\n<ul>\n<li>Use an algebraic equation to solve a basic percent question<\/li>\n<li>Use an algebraic equation to solve application problems involving percent<\/li>\n<\/ul>\n<\/div>\n<h2>Percent of a Whole<\/h2>\n<p>Percents are the ratio of a number and 100. Percents are used in many different applications. Percents are used widely to describe how something changed. For example, you may have heard that the amount of rainfall this month had decreased by 12% from last year, or that the number of jobless claims has increase by 5% this quarter over last quarter.<\/p>\n<div id=\"attachment_3014\" style=\"width: 310px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-3014\" class=\"wp-image-3014 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/117\/2016\/04\/20194605\/Screen-Shot-2016-04-20-at-12.44.43-PM-300x209.png\" alt=\"A graph showing the seasonally adjusted unemployment rate, with the y-axis representing percent from 4 to 10 and the x-axis representing time in years.\" width=\"300\" height=\"209\" \/><\/p>\n<p id=\"caption-attachment-3014\" class=\"wp-caption-text\">Unemployment rate as percent by year between 2004 and 2014.<\/p>\n<\/div>\n<p>We regularly use this kind of language to quickly describe how much something increased or decreased over time or between significant events.<\/p>\n<p>Before we dissect the methods for finding percent change of a quantity, let&#8217;s learn the basics of finding percent of a whole.<\/p>\n<p>For example, if we knew a gas tank held 14 gallons, and wanted to know how many gallons were in [latex]\\frac{1}{4}[\/latex]\u00a0of a tank, we would find [latex]\\frac{1}{4}[\/latex]\u00a0of 14 gallons by multiplying:<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{1}{4}\\,\\cdot \\,14=\\frac{1}{4}\\,\\cdot \\,\\frac{14}{1}=\\frac{14}{4}=3\\frac{2}{4}=3\\frac{1}{2}\\,\\,\\,\\text{gallons}[\/latex]<\/p>\n<p>Likewise, if we wanted to find 25% of 14 gallons, we could find this by multiplying, but first we would need to convert the 25% to a decimal:<\/p>\n<p style=\"text-align: center;\">[latex]25\\%\\,\\,\\text{of}\\,\\,14\\,\\,\\,\\text{gallons}=0.25\\,\\cdot \\,14=3.5\\,\\,\\,\\text{gallons}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox shaded\">\n<h3>Finding a Percent of a Whole<\/h3>\n<p>To find a percent of a whole,<\/p>\n<ul>\n<li>Write the percent as a decimal by moving the decimal two places to the left<\/li>\n<li>Then multiply the percent by the whole amount<\/li>\n<\/ul>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example 1<\/h3>\n<p>What is 10% of $200?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q834578\">Show Solution<\/span><\/p>\n<div id=\"q834578\" class=\"hidden-answer\" style=\"display: none\">Write as a decimal.\u00a0Move the decimal point two places to the left.<\/p>\n<p style=\"text-align: center;\">[latex]10\\%=0.10[\/latex]<\/p>\n<p>Multiply the decimal form of the percent by the whole number.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}0.10\\cdot200\\\\20\\end{array}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>10% of $200 is $20.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Notice in the example above that 10% of 200 is 20. Finding 10% of a number is one of the easiest percentages to calculate.\u00a0To calculate\u00a0<b>10 percent of a number<\/b>, we always simply divide it by\u00a0<b>10<\/b>\u00a0or <strong>move the decimal point one place to the left.<\/strong>\u00a0 For example, 10% of 325 is 32.5.\u00a0 Being able to recall what 10% of a value is might often be helpful when reflecting on the reasonableness of your answers to problems involving different percentages as you will see in some examples in this section.<\/p>\n<p>The following video contains an example that is similar to the one above.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Find the Percent of a Number\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/jTM7ZMvAzsc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<h2>Use an algebraic equation to solve a basic percent question<\/h2>\n<p>From the previous examples, we can identify\u00a0some important parts to finding the percent of a whole. We are going to focus on the equation method to solve problems involving percent.\u00a0 To translate the following problems into equations, we need to know a few key words and what they mean.<\/p>\n<ul>\n<li><strong>\u201cof\u201d<\/strong> means multiply<\/li>\n<li><strong>\u201cis\u201d<\/strong> means equals<\/li>\n<li><strong>\u201cwhat\u201d<\/strong> can be represented by the variable<\/li>\n<\/ul>\n<p>The following examples show how to use an algebraic equation to solve a basic percent question:<\/p>\n<div class=\"textbox exercises\">\n<h3>Example 2<\/h3>\n<p>What is 12% of 270?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q791982\">Show Answer<\/span><\/p>\n<div id=\"q791982\" class=\"hidden-answer\" style=\"display: none\">\n<p>In this question, we will replace:<\/p>\n<p><span style=\"color: #ff0000;\"><strong>\u201cwhat\u201d<\/strong><\/span> with the variable [latex]x[\/latex],<\/p>\n<p><span style=\"color: #008000;\"><strong>\u201cis\u201d<\/strong><\/span> with the equals sign,<\/p>\n<p><span style=\"color: #0000ff;\"><strong>\u201cof\u201d<\/strong><\/span> with the multiplication symbol.<\/p>\n<p>We also need to convert the percentage into a decimal number before writing it in our equation.\u00a0 To convert a percentage to a decimal number, we move the decimal two places to the left.\u00a0 Why is it two places?\u00a0 Percent means \u201cper hundred.\u201d\u00a0 Therefore, 12% means 12\/100.\u00a0 Dividing 12 by 100 gives the result of 0.12.\u00a0 Since we will always be dividing by 100 to convert percentages to decimal numbers, we will always move the decimal two places to the left.<\/p>\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">What<\/span> <span style=\"color: #008000;\">is<\/span><\/strong> 12% <strong><span style=\"color: #0000ff;\">of<\/span><\/strong> 270?<\/p>\n<p style=\"text-align: center;\">[latex]{\\color{red}x}\\hspace{.04in} {\\mathbf{\\color{green}=}}\\hspace{.04in}0.12\\hspace{.03in}\\vcenter{\\hbox{$\\scriptscriptstyle \\color{blue} \\bullet$}}\\hspace{.03in}270[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]x=32.4[\/latex]<\/p>\n<p style=\"text-align: center;\">32.4 is 12% of 270<\/p>\n<p>*Reflect on your answer and make sure it is reasonable! We can recall that 10% of 270 would be 27.0, so since 12% is just a slightly larger percentage than 10%, it makes sense that 32.5 (which is slightly bigger than 27) is 12% of the number 270.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example 3<\/h3>\n<p>30 is 20% of what number?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q204160\">Show Solution<\/span><\/p>\n<div id=\"q204160\" class=\"hidden-answer\" style=\"display: none\">\n<p>In this question, we will replace:<\/p>\n<p><span style=\"color: #ff0000;\"><strong>\u201cwhat number\u201d<\/strong><\/span> with the variable [latex]x[\/latex],<\/p>\n<p><span style=\"color: #008000;\"><strong>\u201cis\u201d<\/strong><\/span> with the equals sign,<\/p>\n<p><span style=\"color: #0000ff;\"><strong>\u201cof\u201d<\/strong><\/span> with the multiplication symbol.<\/p>\n<p style=\"text-align: center;\">30 <span style=\"color: #008000;\"><strong>is<\/strong><\/span> 20% <span style=\"color: #0000ff;\"><strong>of<\/strong><\/span> <span style=\"color: #ff0000;\"><strong>what number?<\/strong><\/span><\/p>\n<p style=\"text-align: center;\">[latex]30\\hspace{.04in}{\\mathbf{\\color{green} =}}\\hspace{.04in}0.20\\hspace{.03in}\\vcenter{\\hbox{$\\scriptscriptstyle \\color{blue} \\bullet$}}\\hspace{.03in}{\\color{red} x}[\/latex]<\/p>\n<p style=\"text-align: left;\">Solve for x by dividing by both sides by 0.20<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{30}{0.20}=\\frac{0.20\\cdot x}{0.20}[\/latex]<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #000000;\">[latex]150=x[\/latex]<\/span><\/p>\n<h4>Answer<\/h4>\n<p>30 is 20% of 150.<\/p>\n<p>*Reflect on your answer to see if it is reasonable! The problem stated that 30 is 20% of some number. If 30 is a percentage of a number, that means it is a portion of the whole. The number we are finding must be <em>larger than<\/em> 30. We can recall that 30 is 10% of 300. It makes sense then that is 30 equates to 20% of 150.\u00a0 Our answer of 150 is reasonable. 30 is 20% of 150.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>The previous problem states that 30 is a portion of another number.\u00a0 Note that this problem could be rewritten: 20% of what number is 30?<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example 4<\/h3>\n<p>What percent of 72 is 9?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q850317\">Show Solution<\/span><\/p>\n<div id=\"q850317\" class=\"hidden-answer\" style=\"display: none\">\n<p>In this question, we will replace:<\/p>\n<p><span style=\"color: #ff0000;\"><strong>\u201cwhat percent\u201d<\/strong><\/span> with the variable [latex]x[\/latex],<\/p>\n<p><span style=\"color: #008000;\"><strong>\u201cis\u201d<\/strong><\/span> with the equals sign,<\/p>\n<p><span style=\"color: #0000ff;\"><strong>\u201cof\u201d<\/strong><\/span> with the multiplication symbol.<\/p>\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">What percent<\/span> <span style=\"color: #0000ff;\">of<\/span><\/strong> 72 <strong><span style=\"color: #008000;\">is<\/span><\/strong> 9?<\/p>\n<p style=\"text-align: center;\">[latex]{\\color{red}x}\\hspace{.03in}\\vcenter{\\hbox{$\\scriptscriptstyle \\color{blue} \\bullet$}}\\hspace{.03in}72\\hspace{.04in}{\\mathbf{\\color{green}=}}\\hspace{.04in}9[\/latex]<\/p>\n<p>Divide to undo the multiplication of x times 72.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{x\\cdot 72}{72}=\\frac{9}{72}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]x=\\frac{9}{72}[\/latex]<\/p>\n<p>Divide 9 by 72 to find the value for x, the unknown.<\/p>\n<p style=\"text-align: center;\">[latex]x=0.125[\/latex]<\/p>\n<p>Since we are looking for a percent, we need to convert the decimal answer we got for x into a percentage. We do that by moving the decimal two places to the right. In order to convert a decimal to a percent, we multiply by 100. Multiplying by 100 always moves the decimal two places to the right.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}x=0.125\\\\x=12.5\\%\\end{array}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<h4>Answer<\/h4>\n<p>12.5% of 72 is 9.<\/p>\n<p>*Reflect on your answer to see if it is reasonable! From what is given, we know that 9 is a portion of 72. Use 10% to see if it gets you close to the answer. We might recall that 7.2 is 10% of 72 so it makes sense that 9 (which is slightly larger that 7.2) would be a slightly larger percentage of 72, at 12.5%. Our answer makes sense!<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Below are some additional video examples to view:<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Example 1:  Solve a Percent Problem Using a Percent Equation\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/A_IHTwXWXl0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Example 2:  Solve a Percent Problem Using a Percent Equation\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/ke4ZTaI1wt8?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Example 3:  Solve a Percent Problem Using a Percent Equation\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/3x4K9zggNt8?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Try some of the examples on your own before revealing the answer.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example 5<\/h3>\n<p>What is 110% of 24?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q108201\">Show Solution<\/span><\/p>\n<div id=\"q108201\" class=\"hidden-answer\" style=\"display: none\">\n<p>In this question, we will replace:<\/p>\n<p><span style=\"color: #ff0000;\"><strong>\u201cwhat\u201d<\/strong><\/span> with the variable [latex]x[\/latex],<\/p>\n<p><span style=\"color: #008000;\"><strong>\u201cis\u201d<\/strong><\/span> with the equals sign,<\/p>\n<p><span style=\"color: #0000ff;\"><strong>\u201cof\u201d<\/strong><\/span> with the multiplication symbol.<\/p>\n<p style=\"text-align: center;\"><span style=\"color: #ff0000;\"><strong>What<\/strong><\/span> <strong><span style=\"color: #008000;\">is<\/span> <\/strong>110% <strong><span style=\"color: #0000ff;\">of<\/span><\/strong> 24?<\/p>\n<p style=\"text-align: center;\">[latex]{\\color{red}x}\\hspace{.04in}{\\mathbf{\\color{green}=}}\\hspace{.04in}1.10\\hspace{.03in}\\vcenter{\\hbox{$\\scriptscriptstyle \\color{blue} \\bullet$}}\\hspace{.03in}24[\/latex]<\/p>\n<p>Write the percent as a decimal by moving the decimal point two places to the left.<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">[latex]x = 1.10 \\cdot 24[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]x = 1.10 \\cdot 24[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]x = 26.4[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>26.4 is 110% of 24.<\/p>\n<p>* Reflect on your answer to see if it is reasonable! This problem is a little easier to estimate. 100% of 24 is 24. And 110% is a little bit more than 24. So, 26.4 is a reasonable answer.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example 6<\/h3>\n<p>What percent of 70.52 is 13.27?\u00a0 Round answer to the nearest tenth of a percent.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q272806\">Show Answer<\/span><\/p>\n<div id=\"q272806\" class=\"hidden-answer\" style=\"display: none\">\n<p>In this question, we will replace:<\/p>\n<p><span style=\"color: #ff0000;\"><strong>\u201cwhat percent\u201d<\/strong><\/span> with the variable [latex]x[\/latex],<\/p>\n<p><span style=\"color: #008000;\"><strong>\u201cis\u201d<\/strong><\/span> with the equals sign,<\/p>\n<p><span style=\"color: #0000ff;\"><strong>\u201cof\u201d<\/strong><\/span> with the multiplication symbol.<\/p>\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">What percent<\/span> <span style=\"color: #0000ff;\">of<\/span> <\/strong>70.52 <strong><span style=\"color: #008000;\">is<\/span><\/strong> 13.27?<\/p>\n<p style=\"text-align: center;\">[latex]{\\color{red}x}\\hspace{.03in}\\vcenter{\\hbox{$\\scriptscriptstyle \\color{blue} \\bullet$}}\\hspace{.03in}70.52 \\hspace{.04in}{\\mathbf{\\color{green}=}}\\hspace{.04in}13.27[\/latex]<\/p>\n<p>Divide to undo the multiplication of x times 70.52.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{x\\cdot 70.52}{70.52}=\\frac{13.27}{70.52}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]x=\\frac{13.27}{70.52}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]x=0.1881735...[\/latex]<\/p>\n<p>Since we are trying to find &#8220;what percent&#8221;, convert our answer to a percentage BEFORE rounding.\u00a0 We do that by moving the decimal two places to the right.\u00a0 In order to convert a decimal to a percent, we multiply by 100.\u00a0 Multiplying by 100 always moves the decimal two places to the right.<\/p>\n<p style=\"text-align: center;\">[latex]x=18.81735..\\%[\/latex]<\/p>\n<p>Round to the nearest tenth of a percent<\/p>\n<p style=\"text-align: center;\">[latex]x=18.8\\%[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div><\/div>\n<h2 class=\"textbox shaded\"><strong>Note:<\/strong> Often times, problems like the ones in this section will ask you to round your final answer. If you need a review on rounding, refer back to Module 0 of this textbook:\u00a0 <a href=\"https:\/\/courses.lumenlearning.com\/slcc-elementaryalgebra\/chapter\/rounding-decimals\/\">Module 0: Rounding Decimals Review<\/a><\/h2>\n<h2>Use an algebraic equation to solve application problems involving percent<\/h2>\n<p>Percents have a wide variety of applications to everyday life, showing up regularly in taxes, discounts, markups, and interest rates. We will look at several examples of how to use percent to calculate markups, discounts, and interest earned or owed.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example 7<\/h3>\n<p>Jeff has a coupon at the Guitar Store for 15% off any purchase of $100 or more. He wants to buy a used guitar that has a price tag of $220 on it. Jeff wonders how much money the coupon will take off of the $220 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\">First, we need to identify what it is we are being asked to find.\u00a0 We can summarize the problem with the question,<\/p>\n<p style=\"text-align: center;\">What is 15% of $220?<\/p>\n<p>Once we identify that question, we can translate it into an equation.<\/p>\n<p>In this question, we will replace:<\/p>\n<p><span style=\"color: #ff0000;\"><strong>\u201cwhat\u201d<\/strong><\/span> with the variable [latex]x[\/latex],<\/p>\n<p><span style=\"color: #008000;\"><strong>\u201cis\u201d<\/strong><\/span> with the equals sign,<\/p>\n<p><span style=\"color: #0000ff;\"><strong>\u201cof\u201d<\/strong><\/span> with the multiplication symbol.<\/p>\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">What<\/span> <span style=\"color: #008000;\">is<\/span><\/strong> 15% <strong><span style=\"color: #0000ff;\">of<\/span> <\/strong>$220?<\/p>\n<p style=\"text-align: center;\">[latex]{\\color{red}x}\\hspace{.04in}{\\mathbf{\\color{green}=}}\\hspace{.04in}15\\hbox{%}\\hspace{.03in}\\vcenter{\\hbox{$\\scriptscriptstyle \\color{blue} \\bullet$}}\\hspace{.03in}220[\/latex]<\/p>\n<p>Convert 15% to 0.15, then multiply by 220.<\/p>\n<p style=\"text-align: center;\">[latex]x= 0.15\\cdot220=33[\/latex]<\/p>\n<p>So, 15% of $220 is $33.<\/p>\n<h4>Answer<\/h4>\n<p>The coupon will take $33 off the original price.<br \/>\n*You can estimate to see if the answer is reasonable. Since 15% is half way between 10% and 20%, 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, 33, is between 22 and 44. So $33 seems reasonable.\n<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example 8<\/h3>\n<p>Tracey paid $185 for an item that was originally priced at $390.\u00a0 What percent of the original price did Tracey pay?\u00a0 Round answer to the nearest tenth of a percent.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q30765\">Show Answer<\/span><\/p>\n<div id=\"q30765\" class=\"hidden-answer\" style=\"display: none\">\u00a0We can summarize the problem with the question,<\/p>\n<p style=\"text-align: center;\">What percent of $390 is $185?<\/p>\n<p>Once we identify that question, we can translate it into an equation.<\/p>\n<p>In this question, we will replace:<\/p>\n<p><span style=\"color: #ff0000;\"><strong>\u201cwhat percent\u201d<\/strong><\/span> with the variable [latex]x[\/latex],<\/p>\n<p><span style=\"color: #008000;\"><strong>\u201cis\u201d<\/strong><\/span> with the equals sign,<\/p>\n<p><span style=\"color: #0000ff;\"><strong>\u201cof\u201d<\/strong><\/span> with the multiplication symbol.<\/p>\n<p style=\"text-align: center;\"><strong><span style=\"color: #ff0000;\">What percent<\/span> <span style=\"color: #0000ff;\">of<\/span> <\/strong>$390 <strong><span style=\"color: #008000;\">is<\/span><\/strong> $185?<\/p>\n<p style=\"text-align: center;\">[latex]{\\color{red}x}\\hspace{.03in}\\vcenter{\\hbox{$\\scriptscriptstyle \\color{blue} \\bullet$}}\\hspace{.03in}390\\hspace{.04in}{\\mathbf{\\color{green}=}} 185[\/latex]<\/p>\n<p>Divide to undo the multiplication of x times 390.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{x\\cdot 390}{390}=\\frac{185}{390}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]x=\\frac{185}{390}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]x=0.474358974...[\/latex]<\/p>\n<p>Since we are looking for a percent, we still need to convert this decimal answer into a percent.\u00a0 Remember we do that by moving the decimal two places to the right.<\/p>\n<p style=\"text-align: center;\">[latex]x=47.4358974..\\%[\/latex]<\/p>\n<p>Round to the nearest tenth of a percent<\/p>\n<p style=\"text-align: center;\">[latex]x=47.4\\%[\/latex]<\/p>\n<p>Tracey paid 47.4% of the original price.<\/p>\n<p>*Reflect if your answer is reasonable! We can find 50% fairly easily by dividing $390 by 2. We see that $195 is 50% of $390, so it makes sense that $185 (which is a little less than $195), is about 47.4% of $390 (which is a little less than 50%).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/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-6993\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li><strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) . <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/3x4K9zggNt8\">https:\/\/youtu.be\/3x4K9zggNt8<\/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><strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) . <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/A_IHTwXWXl0\">https:\/\/youtu.be\/A_IHTwXWXl0<\/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><strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) . <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/ke4ZTaI1wt8\">https:\/\/youtu.be\/ke4ZTaI1wt8<\/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>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":348856,"menu_order":9,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"\",\"author\":\"James Sousa (Mathispower4u.com) \",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/3x4K9zggNt8\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"\",\"author\":\"James Sousa (Mathispower4u.com) \",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/A_IHTwXWXl0\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"\",\"author\":\"James Sousa (Mathispower4u.com) \",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/ke4ZTaI1wt8\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-6993","chapter","type-chapter","status-publish","hentry"],"part":17,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-elementaryalgebra\/wp-json\/pressbooks\/v2\/chapters\/6993","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-elementaryalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-elementaryalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-elementaryalgebra\/wp-json\/wp\/v2\/users\/348856"}],"version-history":[{"count":86,"href":"https:\/\/courses.lumenlearning.com\/slcc-elementaryalgebra\/wp-json\/pressbooks\/v2\/chapters\/6993\/revisions"}],"predecessor-version":[{"id":9598,"href":"https:\/\/courses.lumenlearning.com\/slcc-elementaryalgebra\/wp-json\/pressbooks\/v2\/chapters\/6993\/revisions\/9598"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-elementaryalgebra\/wp-json\/pressbooks\/v2\/parts\/17"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-elementaryalgebra\/wp-json\/pressbooks\/v2\/chapters\/6993\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-elementaryalgebra\/wp-json\/wp\/v2\/media?parent=6993"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-elementaryalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=6993"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-elementaryalgebra\/wp-json\/wp\/v2\/contributor?post=6993"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-elementaryalgebra\/wp-json\/wp\/v2\/license?post=6993"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}