{"id":4771,"date":"2017-12-27T00:03:57","date_gmt":"2017-12-27T00:03:57","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/cuny-hunter-collegealgebra\/?post_type=chapter&#038;p=4771"},"modified":"2017-12-27T00:12:46","modified_gmt":"2017-12-27T00:12:46","slug":"percent-review","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/chapter\/percent-review\/","title":{"raw":"Percent Review","rendered":"Percent Review"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Explain the basics of percents\r\n<ul>\r\n \t<li>Find a percent of a whole<\/li>\r\n \t<li>Identify the amount, the base, and the percent in a percent problem<\/li>\r\n \t<li>Find the unknown in a percent problem<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Solve equations containing percents\r\n<ul>\r\n \t<li>Identify the unknown in a percent problem<\/li>\r\n \t<li>Write a percent equation<\/li>\r\n \t<li>Solve equations with percent<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Solve percent change and interest problems\r\n<ul>\r\n \t<li>Calculate discounts and markups using percent<\/li>\r\n \t<li>Calculate interest earned or owed<\/li>\r\n \t<li>Read and interpret data from pie charts as percents<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n&nbsp;\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 unemployment rate, with the y-axis representing percent and the x-axis representing time.\" 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\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<\/h3>\r\nWhat is 15% 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]15\\%=0.15[\/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}0.15\\cdot200\\\\30\\end{array}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n15% of $200 is $30\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe following video contains an example that is similar to the one above.\r\n\r\nhttps:\/\/youtu.be\/jTM7ZMvAzsc\r\n\r\nFrom the previous example, we can identify\u00a0three important parts to finding the percent of a whole:\r\n<ul>\r\n \t<li>the <b>percent<\/b>,\u00a0<b> <\/b>has the percent symbol (%) or the word \u201cpercent\u201d<\/li>\r\n \t<li>the <b>amount<\/b>, the amount is\u00a0part of the whole<\/li>\r\n \t<li>and the <b>base, <\/b>the base is the whole amount<\/li>\r\n<\/ul>\r\nThe following examples show how to identify the three parts: the percent, the base, and the amount.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nIdentify the percent, amount, and base in this problem.\r\n\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\n<b>Percent:<\/b> The percent is the number with the % symbol: <b>20%<\/b>.\r\n\r\n<b>Base:<\/b> The base is the whole amount, which in this case is unknown.\r\n\r\n<b>Amount:<\/b> The amount based on the percent is <b>30<\/b>.\r\n<h4>Answer<\/h4>\r\nPercent = 20%\r\nAmount = 30\r\nBase = unknown\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe previous problem states that 30 is a portion of another number. That means 30 is the amount. 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<\/h3>\r\nIdentify the percent, amount, and base in this problem.\r\n\r\nWhat percent of 30 is 3?\r\n\r\n[reveal-answer q=\"318375\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"318375\"]\r\n\r\n<b>Percent:<\/b> The percent is unknown, because the problem states \u201cwhat percent?\u201d.\r\n\r\n<b>Base:<\/b> The base is the whole amount, so the base is 30.\r\n\r\n<b>Amount:<\/b> The amount is a portion of the whole, which is 3 in this case.\r\n<h4>Answer<\/h4>\r\nPercent = unknown\r\nAmount = 3\r\nBase = 30\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nIdentify the percent, amount, and base in this problem.\r\n\r\nWhat is 60% of 45?\r\n\r\n[reveal-answer q=\"102763\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"102763\"]\r\n\r\n<b>Percent:<\/b> The percent is known\r\n\r\n<b>Base:\u00a0<\/b>The base is the whole amount, so the base is 45.\r\n\r\n<b>Amount:<\/b> The amount is a portion of the whole, which is what we want to identify.\r\n<h4>Answer<\/h4>\r\nPercent =\u00a060%\r\nAmount = unknown\r\nBase = 45\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe following video provides more examples that describe how to identify the percent, amount, and base in a percent problem.\r\n\r\nhttps:\/\/youtu.be\/zwT58-LJCvs\r\n\r\nIn the next section, you will use the parts of a percent problem to find the percent increase or decrease of a quantity by writing and solving equations.\r\n<h2>Percent Equations<\/h2>\r\nPercent problems can be solved by writing <strong>equations<\/strong>. An equation uses an equal sign (=) to show that two mathematical expressions have the same value.\r\n\r\nPercents are fractions, and just like fractions, when finding a percent (or fraction, or portion) of another amount, you multiply.\r\n\r\nIn the previous section, we identified\u00a0three important parts to finding the percent of a whole:\r\n<ul>\r\n \t<li>the <strong>percent<\/strong>,\u00a0has the percent symbol (%) or the word \u201cpercent\u201d<\/li>\r\n \t<li>the <strong>amount<\/strong>, the amount is\u00a0part of the whole<\/li>\r\n \t<li>and the <strong>base<\/strong>, the base is the whole amount<\/li>\r\n<\/ul>\r\nUsing these parts, we can define equations that will help us answer percent problems.\r\n<div class=\"textbox shaded\">\r\n<h3>The Percent Equation<\/h3>\r\nPercent of the Base is the Amount.\r\n<p style=\"text-align: center\">[latex]\\text{Percent}\\cdot\\text{Base}=\\text{Amount}[\/latex]<\/p>\r\n\r\n<\/div>\r\nIn the examples below, the unknown is represented by the letter <i>n.<\/i> The unknown can be represented by any letter or a box \u25a1, question mark, or even a smiley face :)\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nWrite an equation that represents the following problem.\r\n<p style=\"text-align: center\">30 is 20% of what number?<\/p>\r\n[reveal-answer q=\"671134\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"671134\"]Rewrite the problem in the form \u201cpercent of base is amount.\u201d\r\n<p style=\"text-align: center\">20% of what number is 30?<\/p>\r\nIdentify the percent, the base, and the amount.\r\n\r\nPercent is: 20%\r\nBase is: unknown\r\nAmount is: 30\r\n\r\nWrite the percent equation. using <i>n<\/i> for the base, which is the unknown value.\r\n<p style=\"text-align: center\">[latex]\\text{Percent}\\cdot\\text{Base}=\\text{Amount}[\/latex]<\/p>\r\n<p style=\"text-align: center\">[latex]20\\%\\cdot{n}=30[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]20\\%\\cdot{n}=30[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe following example shows how to use the percent equation to find the base in a percent equation.\r\n\r\nhttps:\/\/youtu.be\/3etjmUw8K3A\r\n\r\nOnce you have an equation, you can solve it and find the unknown value. For example, to solve\r\n[latex]20%\\cdot{n}=30[\/latex]\r\n\r\nyou can divide 30 by 20% to find the unknown:\r\n<p style=\"text-align: center\">[latex]20\\%\\cdot{n}=30[\/latex]<\/p>\r\nYou can solve this by writing the percent as a decimal or fraction and then dividing.\r\n<p style=\"text-align: center\">[latex]20\\%\\cdot{n}=30[\/latex]<\/p>\r\n<p style=\"text-align: center\">[latex]n=30\\div20\\%=30\\div0.20=150[\/latex]<\/p>\r\n\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/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\"]Identify the percent, base, and amount.\r\n\r\nPercent: unknown\r\nBase: 72\r\nAmount: 9\r\n\r\nWrite the percent equation: Percent [latex]\\cdot[\/latex] Base = Amount. Use <i>n<\/i> for the unknown (percent).\r\n<p style=\"text-align: center\">[latex]n\\cdot72=9[\/latex]<\/p>\r\nDivide to undo the multiplication of <i>n<\/i> times 72.\r\n<p style=\"text-align: center\">[latex]n=\\frac{9}{72}[\/latex]<\/p>\r\nDivide 9 by 72 to find the value for <em>n<\/em>, the unknown.\r\n<p style=\"text-align: center\">[latex] \\displaystyle 72\\overset{0.125}{\\overline{\\left){9.000}\\right.}}[\/latex]<\/p>\r\nMove the decimal point two places to the right to write the decimal as a percent.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{c}n=0.125\\\\n=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[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video example, you are shown how to use the percent equation to find the base in a percent problem.\r\n\r\nhttps:\/\/youtu.be\/p2KHHFMhJRs\r\nYou can estimate to see if the answer is reasonable. Use 10% and 20%, numbers close to 12.5%, to see if they get you close to the answer.\r\n\r\n10% of 72 = 0.1 \u00b7 72 = 7.2\r\n\r\n20% of 72 = 0.2 \u00b7 72 = 14.4\r\n\r\nNotice that 9 is between 7.2 and 14.4, so 12.5% is reasonable since it is between 10% and 20%.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/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\"]Identify the percent, the base, and the amount.\r\n\r\nPercent: 110%\r\nBase: 24\r\nAmount: unknown\r\n\r\nWrite the percent equation.\r\n<p style=\"text-align: center\">[latex]\\text{Percent}\\cdot\\text{Base}=\\text{Amount}[\/latex]<\/p>\r\nThe amount is unknown, so use <i>n<\/i>.\r\n<p style=\"text-align: center\">110% \u00b7 24 = <i>n<\/i><\/p>\r\nWrite the percent as a decimal by moving the decimal point two places to the left.\r\n\r\nMultiply 24 by 1.10 or 1.1.\r\n<p style=\"text-align: center\">1.10 \u00b7 24 = <i>n<\/i><\/p>\r\n<p style=\"text-align: center\">1.10 \u00b7 24 = 26.4 = <i>n<\/i><\/p>\r\n\r\n<h4>Answer<\/h4>\r\n26.4 is 110% of 24.\r\n\r\nThis 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\nThe video that follows shows how top use the percent equation to find the amount in a percent equation.\r\n\r\nhttps:\/\/youtu.be\/dO3AaW_c9s0\r\n\r\n&nbsp;\r\n<h2>Percent Change<\/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<\/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\"]Simplify the problems by eliminating extra words.\r\n<p style=\"text-align: center\">How much is 15% of $220?<\/p>\r\nIdentify the percent, the base, and the amount.\r\n\r\nPercent: 15%\r\nBase: 220\r\nAmount: <i>n<\/i>\r\n\r\nWrite the percent equation.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{c}\\text{Percent}\\cdot\\text{Base}=\\text{Amount}\\\\15\\%\\cdot220=n\\end{array}[\/latex]<\/p>\r\nConvert 15% to 0.15, then multiply by 220. 15% of $220 is $33.\r\n<p style=\"text-align: center\">[latex]0.15\\cdot220=33[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\nThe coupon will take $33 off the original price.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe example video that follows shows how to use the percent equation to find the amount of a discount from the price of a phone.\r\n\r\nhttps:\/\/youtu.be\/bC7GUc1K6LU\r\n\r\nYou 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\r\nThere are many other situations that involve percents. Below are just a few.\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 $31.50, which included 5% 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: 105%\r\nBase: <i>n<\/i>\r\nAmount: 31.50\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 105% 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 1.05.\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 $30 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<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSusana worked 20 hours at her job last week. This week, she worked 35 hours. In terms of a percent, how much more did she work this week than last week?\r\n\r\n[reveal-answer q=\"811296\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"811296\"]Simplify the problem by eliminating extra words.\r\n<p style=\"text-align: center\">35 is what percent of 20?<\/p>\r\nIdentify the percent, the base, and the amount.\r\n\r\nPercent: <i>n<\/i>\r\nBase: 20\r\nAmount: 35\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}\\\\n\\cdot20=35\\end{array}[\/latex]<\/p>\r\nDivide to undo the multiplication of <i>n<\/i> times 20.\r\n<p style=\"text-align: center\">[latex]n=35\\div20[\/latex]<\/p>\r\nConvert 1.75 to a percent.\r\n<p style=\"text-align: center\">[latex]n=1.75=175\\%[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\nSince 35 is 175% of 20, Susana worked 75% more this week than she did last week. (You can think of this as \u201cSusana worked 100% of the hours she worked last week, as well as 75% more.\u201d)\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe video that follows explains how to use the percent equation to determine the percent increase of a given amount.\r\n\r\nhttps:\/\/youtu.be\/6YYpqlSiF74\r\n\r\n<h2>Pie Charts<\/h2>\r\nCircle graphs, or pie charts, represent data as sections of the circle (or \u201cpieces of the pie\u201d), corresponding to their percentage of the whole. Circle graphs are often used to show how a whole set of data is broken down into individual components.\r\n\r\nHere\u2019s an example. At the beginning of a semester, a teacher talks about how she will determine student grades. She says, \u201cHalf your grade will be based on the final exam and 20% will be determined by quizzes. A class project will also be worth 20% and class participation will count for 10%.\u201d In addition to telling the class this information, she could also create a circle graph.\r\n<p align=\"center\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/117\/2016\/04\/20210251\/image074.gif\" width=\"373\" height=\"264\" \/><\/p>\r\nThis graph is useful because it relates each part\u2014the final exam, the quizzes, the class project, and the class participation\u2014to the whole.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nIf the total number of points possible in the class is 500, how many points is the final exam worth?\r\n\r\n[reveal-answer q=\"956080\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"956080\"]Simplify the problem by eliminating extra words.\r\n<p style=\"text-align: center\">What is 50% of 500?<\/p>\r\nIdentify the percent, the base, and the amount.\r\n\r\nPercent: <i>50% = 0.50<\/i>\r\nBase: 500\r\nAmount:\u00a0n\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}\\\\0.50\\cdot500=n\\end{array}[\/latex]<\/p>\r\nMultiply.\r\n<p style=\"text-align: center\">[latex]\\left(0.50\\right)\\left(500\\right) = n[\/latex]<\/p>\r\n<p style=\"text-align: center\">[latex]250 = n[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\nThis tells us that the final is worth 250 points.\r\n<p style=\"text-align: center\">[\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\nIn the following video, an example of using a pie chart to determine a percent of a whole is shown.\r\n\r\nhttps:\/\/youtu.be\/TAUDMvl8Vg8\r\n<h2>Summary<\/h2>\r\nWhen solving application problems with percents, it is important to be extremely careful in identifying the percent, whole, and amount in the problem. Once those are identified, use the percent equation to solve the problem. Write your final answer back in terms of the original scenario.\r\n","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Explain the basics of percents\n<ul>\n<li>Find a percent of a whole<\/li>\n<li>Identify the amount, the base, and the percent in a percent problem<\/li>\n<li>Find the unknown in a percent problem<\/li>\n<\/ul>\n<\/li>\n<li>Solve equations containing percents\n<ul>\n<li>Identify the unknown in a percent problem<\/li>\n<li>Write a percent equation<\/li>\n<li>Solve equations with percent<\/li>\n<\/ul>\n<\/li>\n<li>Solve percent change and interest problems\n<ul>\n<li>Calculate discounts and markups using percent<\/li>\n<li>Calculate interest earned or owed<\/li>\n<li>Read and interpret data from pie charts as percents<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;\n<\/p><\/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 unemployment rate, with the y-axis representing percent and the x-axis representing time.\" 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<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<\/h3>\n<p>What is 15% 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]15\\%=0.15[\/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}0.15\\cdot200\\\\30\\end{array}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>15% of $200 is $30<\/p>\n<\/div>\n<\/div>\n<\/div>\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>From the previous example, we can identify\u00a0three important parts to finding the percent of a whole:<\/p>\n<ul>\n<li>the <b>percent<\/b>,\u00a0<b> <\/b>has the percent symbol (%) or the word \u201cpercent\u201d<\/li>\n<li>the <b>amount<\/b>, the amount is\u00a0part of the whole<\/li>\n<li>and the <b>base, <\/b>the base is the whole amount<\/li>\n<\/ul>\n<p>The following examples show how to identify the three parts: the percent, the base, and the amount.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Identify the percent, amount, and base in this problem.<\/p>\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><b>Percent:<\/b> The percent is the number with the % symbol: <b>20%<\/b>.<\/p>\n<p><b>Base:<\/b> The base is the whole amount, which in this case is unknown.<\/p>\n<p><b>Amount:<\/b> The amount based on the percent is <b>30<\/b>.<\/p>\n<h4>Answer<\/h4>\n<p>Percent = 20%<br \/>\nAmount = 30<br \/>\nBase = unknown<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>The previous problem states that 30 is a portion of another number. That means 30 is the amount. Note that this problem could be rewritten: 20% of what number is 30?<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Identify the percent, amount, and base in this problem.<\/p>\n<p>What percent of 30 is 3?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q318375\">Show Solution<\/span><\/p>\n<div id=\"q318375\" class=\"hidden-answer\" style=\"display: none\">\n<p><b>Percent:<\/b> The percent is unknown, because the problem states \u201cwhat percent?\u201d.<\/p>\n<p><b>Base:<\/b> The base is the whole amount, so the base is 30.<\/p>\n<p><b>Amount:<\/b> The amount is a portion of the whole, which is 3 in this case.<\/p>\n<h4>Answer<\/h4>\n<p>Percent = unknown<br \/>\nAmount = 3<br \/>\nBase = 30<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Identify the percent, amount, and base in this problem.<\/p>\n<p>What is 60% of 45?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q102763\">Show Solution<\/span><\/p>\n<div id=\"q102763\" class=\"hidden-answer\" style=\"display: none\">\n<p><b>Percent:<\/b> The percent is known<\/p>\n<p><b>Base:\u00a0<\/b>The base is the whole amount, so the base is 45.<\/p>\n<p><b>Amount:<\/b> The amount is a portion of the whole, which is what we want to identify.<\/p>\n<h4>Answer<\/h4>\n<p>Percent =\u00a060%<br \/>\nAmount = unknown<br \/>\nBase = 45<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>The following video provides more examples that describe how to identify the percent, amount, and base in a percent problem.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Identify the Percent, Base, and Amount of a Percent Question\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/zwT58-LJCvs?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>In the next section, you will use the parts of a percent problem to find the percent increase or decrease of a quantity by writing and solving equations.<\/p>\n<h2>Percent Equations<\/h2>\n<p>Percent problems can be solved by writing <strong>equations<\/strong>. An equation uses an equal sign (=) to show that two mathematical expressions have the same value.<\/p>\n<p>Percents are fractions, and just like fractions, when finding a percent (or fraction, or portion) of another amount, you multiply.<\/p>\n<p>In the previous section, we identified\u00a0three important parts to finding the percent of a whole:<\/p>\n<ul>\n<li>the <strong>percent<\/strong>,\u00a0has the percent symbol (%) or the word \u201cpercent\u201d<\/li>\n<li>the <strong>amount<\/strong>, the amount is\u00a0part of the whole<\/li>\n<li>and the <strong>base<\/strong>, the base is the whole amount<\/li>\n<\/ul>\n<p>Using these parts, we can define equations that will help us answer percent problems.<\/p>\n<div class=\"textbox shaded\">\n<h3>The Percent Equation<\/h3>\n<p>Percent of the Base is the Amount.<\/p>\n<p style=\"text-align: center\">[latex]\\text{Percent}\\cdot\\text{Base}=\\text{Amount}[\/latex]<\/p>\n<\/div>\n<p>In the examples below, the unknown is represented by the letter <i>n.<\/i> The unknown can be represented by any letter or a box \u25a1, question mark, or even a smiley face :)<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Write an equation that represents the following problem.<\/p>\n<p style=\"text-align: center\">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=\"q671134\">Show Solution<\/span><\/p>\n<div id=\"q671134\" class=\"hidden-answer\" style=\"display: none\">Rewrite the problem in the form \u201cpercent of base is amount.\u201d<\/p>\n<p style=\"text-align: center\">20% of what number is 30?<\/p>\n<p>Identify the percent, the base, and the amount.<\/p>\n<p>Percent is: 20%<br \/>\nBase is: unknown<br \/>\nAmount is: 30<\/p>\n<p>Write the percent equation. using <i>n<\/i> for the base, which is the unknown value.<\/p>\n<p style=\"text-align: center\">[latex]\\text{Percent}\\cdot\\text{Base}=\\text{Amount}[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]20\\%\\cdot{n}=30[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]20\\%\\cdot{n}=30[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>The following example shows how to use the percent equation to find the base in a percent equation.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Use a Percent Equation to Solve for a Base or Whole Amount\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/3etjmUw8K3A?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Once you have an equation, you can solve it and find the unknown value. For example, to solve<br \/>\n[latex]20%\\cdot{n}=30[\/latex]<\/p>\n<p>you can divide 30 by 20% to find the unknown:<\/p>\n<p style=\"text-align: center\">[latex]20\\%\\cdot{n}=30[\/latex]<\/p>\n<p>You can solve this by writing the percent as a decimal or fraction and then dividing.<\/p>\n<p style=\"text-align: center\">[latex]20\\%\\cdot{n}=30[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]n=30\\div20\\%=30\\div0.20=150[\/latex]<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/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\">Identify the percent, base, and amount.<\/p>\n<p>Percent: unknown<br \/>\nBase: 72<br \/>\nAmount: 9<\/p>\n<p>Write the percent equation: Percent [latex]\\cdot[\/latex] Base = Amount. Use <i>n<\/i> for the unknown (percent).<\/p>\n<p style=\"text-align: center\">[latex]n\\cdot72=9[\/latex]<\/p>\n<p>Divide to undo the multiplication of <i>n<\/i> times 72.<\/p>\n<p style=\"text-align: center\">[latex]n=\\frac{9}{72}[\/latex]<\/p>\n<p>Divide 9 by 72 to find the value for <em>n<\/em>, the unknown.<\/p>\n<p style=\"text-align: center\">[latex]\\displaystyle 72\\overset{0.125}{\\overline{\\left){9.000}\\right.}}[\/latex]<\/p>\n<p>Move the decimal point two places to the right to write the decimal as a percent.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{c}n=0.125\\\\n=12.5\\%\\end{array}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<h4>Answer<\/h4>\n<p>12.5% of 72 is 9.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the following video example, you are shown how to use the percent equation to find the base in a percent problem.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Use the Percent Equation to Find a Percent\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/p2KHHFMhJRs?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\nYou can estimate to see if the answer is reasonable. Use 10% and 20%, numbers close to 12.5%, to see if they get you close to the answer.<\/p>\n<p>10% of 72 = 0.1 \u00b7 72 = 7.2<\/p>\n<p>20% of 72 = 0.2 \u00b7 72 = 14.4<\/p>\n<p>Notice that 9 is between 7.2 and 14.4, so 12.5% is reasonable since it is between 10% and 20%.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/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\">Identify the percent, the base, and the amount.<\/p>\n<p>Percent: 110%<br \/>\nBase: 24<br \/>\nAmount: unknown<\/p>\n<p>Write the percent equation.<\/p>\n<p style=\"text-align: center\">[latex]\\text{Percent}\\cdot\\text{Base}=\\text{Amount}[\/latex]<\/p>\n<p>The amount is unknown, so use <i>n<\/i>.<\/p>\n<p style=\"text-align: center\">110% \u00b7 24 = <i>n<\/i><\/p>\n<p>Write the percent as a decimal by moving the decimal point two places to the left.<\/p>\n<p>Multiply 24 by 1.10 or 1.1.<\/p>\n<p style=\"text-align: center\">1.10 \u00b7 24 = <i>n<\/i><\/p>\n<p style=\"text-align: center\">1.10 \u00b7 24 = 26.4 = <i>n<\/i><\/p>\n<h4>Answer<\/h4>\n<p>26.4 is 110% of 24.<\/p>\n<p>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<p>The video that follows shows how top use the percent equation to find the amount in a percent equation.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-5\" title=\"Use a Percent Equation to Solve for an Amount or Part of a Whole\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/dO3AaW_c9s0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<h2>Percent Change<\/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<\/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\">Simplify the problems by eliminating extra words.<\/p>\n<p style=\"text-align: center\">How much is 15% of $220?<\/p>\n<p>Identify the percent, the base, and the amount.<\/p>\n<p>Percent: 15%<br \/>\nBase: 220<br \/>\nAmount: <i>n<\/i><\/p>\n<p>Write the percent equation.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{c}\\text{Percent}\\cdot\\text{Base}=\\text{Amount}\\\\15\\%\\cdot220=n\\end{array}[\/latex]<\/p>\n<p>Convert 15% to 0.15, then multiply by 220. 15% of $220 is $33.<\/p>\n<p style=\"text-align: center\">[latex]0.15\\cdot220=33[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>The coupon will take $33 off the original price.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>The example video that follows shows how to use the percent equation to find the amount of a discount from the price of a phone.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-6\" title=\"Percent App:  Find the Amount of Savings from a Discount\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/bC7GUc1K6LU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>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.<\/p>\n<p>There are many other situations that involve percents. Below are just a few.<\/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 $31.50, which included 5% 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: 105%<br \/>\nBase: <i>n<\/i><br \/>\nAmount: 31.50<\/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 105% 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 1.05.<\/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 $30 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-7\" 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<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Susana worked 20 hours at her job last week. This week, she worked 35 hours. In terms of a percent, how much more did she work this week than last week?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q811296\">Show Solution<\/span><\/p>\n<div id=\"q811296\" class=\"hidden-answer\" style=\"display: none\">Simplify the problem by eliminating extra words.<\/p>\n<p style=\"text-align: center\">35 is what percent of 20?<\/p>\n<p>Identify the percent, the base, and the amount.<\/p>\n<p>Percent: <i>n<\/i><br \/>\nBase: 20<br \/>\nAmount: 35<\/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}\\\\n\\cdot20=35\\end{array}[\/latex]<\/p>\n<p>Divide to undo the multiplication of <i>n<\/i> times 20.<\/p>\n<p style=\"text-align: center\">[latex]n=35\\div20[\/latex]<\/p>\n<p>Convert 1.75 to a percent.<\/p>\n<p style=\"text-align: center\">[latex]n=1.75=175\\%[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>Since 35 is 175% of 20, Susana worked 75% more this week than she did last week. (You can think of this as \u201cSusana worked 100% of the hours she worked last week, as well as 75% more.\u201d)<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>The video that follows explains how to use the percent equation to determine the percent increase of a given amount.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-8\" title=\"Find a Percent of Increase Using a Percent Equation\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/6YYpqlSiF74?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Pie Charts<\/h2>\n<p>Circle graphs, or pie charts, represent data as sections of the circle (or \u201cpieces of the pie\u201d), corresponding to their percentage of the whole. Circle graphs are often used to show how a whole set of data is broken down into individual components.<\/p>\n<p>Here\u2019s an example. At the beginning of a semester, a teacher talks about how she will determine student grades. She says, \u201cHalf your grade will be based on the final exam and 20% will be determined by quizzes. A class project will also be worth 20% and class participation will count for 10%.\u201d In addition to telling the class this information, she could also create a circle graph.<\/p>\n<p style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/117\/2016\/04\/20210251\/image074.gif\" width=\"373\" height=\"264\" alt=\"image\" \/><\/p>\n<p>This graph is useful because it relates each part\u2014the final exam, the quizzes, the class project, and the class participation\u2014to the whole.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>If the total number of points possible in the class is 500, how many points is the final exam worth?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q956080\">Show Solution<\/span><\/p>\n<div id=\"q956080\" class=\"hidden-answer\" style=\"display: none\">Simplify the problem by eliminating extra words.<\/p>\n<p style=\"text-align: center\">What is 50% of 500?<\/p>\n<p>Identify the percent, the base, and the amount.<\/p>\n<p>Percent: <i>50% = 0.50<\/i><br \/>\nBase: 500<br \/>\nAmount:\u00a0n<\/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}\\\\0.50\\cdot500=n\\end{array}[\/latex]<\/p>\n<p>Multiply.<\/p>\n<p style=\"text-align: center\">[latex]\\left(0.50\\right)\\left(500\\right) = n[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]250 = n[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>This tells us that the final is worth 250 points.<\/p>\n<p style=\"text-align: center\"><\/div>\n<\/div>\n<\/div>\n<p>In the following video, an example of using a pie chart to determine a percent of a whole is shown.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-9\" title=\"Percent App: Find the Percent of An Amount After Reading a Pie Chart\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/TAUDMvl8Vg8?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Summary<\/h2>\n<p>When solving application problems with percents, it is important to be extremely careful in identifying the percent, whole, and amount in the problem. Once those are identified, use the percent equation to solve the problem. Write your final answer back in terms of the original scenario.<\/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-4771\">\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>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Screenshot: Unemployment Graph. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Find the Percent of a Number. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/jTM7ZMvAzsc\">https:\/\/youtu.be\/jTM7ZMvAzsc<\/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>Identify the Percent, Base, and Amount of a Percent Question. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/zwT58-LJCvs\">https:\/\/youtu.be\/zwT58-LJCvs<\/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>Unit 5: Percents, from Developmental Math: An Open Program. <strong>Provided by<\/strong>: Monterey Institute of Technology and Education. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/dm-opentext\">http:\/\/nrocnetwork.org\/dm-opentext<\/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>Use a Percent Equation to Solve for a Base or Whole Amount. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/3etjmUw8K3A\">https:\/\/youtu.be\/3etjmUw8K3A<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em><\/li><li>Use the Percent Equation to Find a Percent. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/p2KHHFMhJRs\">https:\/\/youtu.be\/p2KHHFMhJRs<\/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>Use a Percent Equation to Solve for an Amount or Part of a Whole. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/dO3AaW_c9s0\">https:\/\/youtu.be\/dO3AaW_c9s0<\/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>Percent App: Find the Amount of Savings from a Discount. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/bC7GUc1K6LU\">https:\/\/youtu.be\/bC7GUc1K6LU<\/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>Percent App: Find a Price Before Tax From Total Price. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/qgafD4z8OUE\">https:\/\/youtu.be\/qgafD4z8OUE<\/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>Find a Percent of Increase Using a Percent Equation. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/6YYpqlSiF74\">https:\/\/youtu.be\/6YYpqlSiF74<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/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":60342,"menu_order":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Find the Percent of a Number\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/jTM7ZMvAzsc\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Identify the Percent, Base, and Amount of a Percent Question\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/zwT58-LJCvs\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Unit 5: Percents, from Developmental Math: An Open Program\",\"author\":\"\",\"organization\":\"Monterey Institute of Technology and Education\",\"url\":\"http:\/\/nrocnetwork.org\/dm-opentext\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Screenshot: Unemployment Graph\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Use a Percent Equation to Solve for a Base or Whole Amount\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/3etjmUw8K3A\",\"project\":\"\",\"license\":\"pd\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Use the Percent Equation to Find a Percent\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/p2KHHFMhJRs\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Use a Percent Equation to Solve for an Amount or Part of a Whole\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/dO3AaW_c9s0\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Percent App: Find the Amount of Savings from a Discount\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/bC7GUc1K6LU\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Percent App: Find a Price Before Tax From Total Price\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/qgafD4z8OUE\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Find a Percent of Increase Using a Percent Equation\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/6YYpqlSiF74\",\"project\":\"\",\"license\":\"pd\",\"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-4771","chapter","type-chapter","status-publish","hentry"],"part":249,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4771","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/wp\/v2\/users\/60342"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4771\/revisions"}],"predecessor-version":[{"id":4772,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4771\/revisions\/4772"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/249"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4771\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/wp\/v2\/media?parent=4771"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=4771"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/wp\/v2\/contributor?post=4771"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-coreq-collegealgebra\/wp-json\/wp\/v2\/license?post=4771"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}