{"id":10429,"date":"2017-05-26T20:35:44","date_gmt":"2017-05-26T20:35:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10429"},"modified":"2020-09-11T00:28:52","modified_gmt":"2020-09-11T00:28:52","slug":"translating-and-solving-basic-percent-equations","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/translating-and-solving-basic-percent-equations\/","title":{"raw":"4.2.a - Translating and Solving Basic Percent Equations","rendered":"4.2.a &#8211; Translating and Solving Basic Percent Equations"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Translate and solve basic percent equations<\/li>\r\n<\/ul>\r\n<\/div>\r\nWe will solve percent equations by using the methods we used to solve equations with fractions or decimals. In the past, you may have solved percent problems by setting them up as proportions. That was the best method available when you did not have the tools of algebra. Now you can translate word sentences into algebraic equations, and then solve the equations.\r\n\r\nRemember, percents are fractions, and just like fractions, when finding a percent (or fraction, or portion) of another amount, you multiply.\r\n\r\n<a href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/understand-percent\/\">In a previous section, we identified\u00a0three important parts to finding the percent of a whole<\/a>:\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\n<h2>Percent of a Whole<\/h2>\r\nWe can use this equation to help us solve equations that require us to find the percent of a whole.\r\n\r\nFor example, if we knew a gas tank held [latex]14[\/latex] 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 [latex]14[\/latex]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 \u00a0[latex]25\\%[\/latex] of [latex]14[\/latex] 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 [latex]15[\/latex]% of $[latex]200[\/latex]?\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\n[latex]15\\%[\/latex] of [latex]\\$200[\/latex] is [latex]\\$30[\/latex]\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\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\r\nIn the next examples, we will find the amount. We must be sure to change the given percent to a decimal when we translate the words into an equation.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWhat number is [latex]\\text{35%}[\/latex] of [latex]90?[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168467117646\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to translate the question 'what number is 35% of 90?'. Translate the words into algebra, letting the variable n equal the number, representing the word 'is' with an equals sign, writing 35% as 0.35, representing the word 'of' with a multiplication dot, and writing 90 as 90. The result is the equation, n = 0.35 \u00b7 90. Multiply to find that n = 31.5. 31.5 is 35% of 90.\">\r\n<tbody>\r\n<tr>\r\n<td>Translate into algebra. Let [latex]n=[\/latex] the number.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221911\/CNX_BMath_Figure_06_02_003_img-01-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]n=31.5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]31.5[\/latex] is [latex]35\\text{%}[\/latex] of [latex]90[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]80094[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\n[latex]\\text{125%}[\/latex] of [latex]28[\/latex] is what number?\r\n[reveal-answer q=\"892746\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"892746\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469855167\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to translate the question '125% of 28 is what number?' Translate the words into algebra, writing 125% as 1.25, representing the word 'of' with a multiplication dot, representing the word 'is' with an equals sign, and letting the variable a equal the number. The result is the equation 1.25 \u00b7 28 = a. Multiply to find that 35 = a. 125% of 28 is 35.\">\r\n<tbody>\r\n<tr>\r\n<td>Translate into algebra. Let [latex]a=[\/latex] the number.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221914\/CNX_BMath_Figure_06_02_004_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]35=a[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]125\\text{%}[\/latex] of [latex]28[\/latex] is [latex]35[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nRemember that a percent over [latex]100[\/latex] is a number greater than [latex]1[\/latex]. We found that [latex]\\text{125%}[\/latex] of [latex]28[\/latex] is [latex]35[\/latex], which is greater than [latex]28[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146672[\/ohm_question]\r\n\r\n<\/div>\r\nThe video that follows shows how to use the percent equation to find the amount in a percent equation when the percent is greater than [latex]100\\%[\/latex].\r\n\r\nhttps:\/\/youtu.be\/dO3AaW_c9s0he\r\n<h2>Solve for the Base<\/h2>\r\nIn the next examples, we are asked to find the base.\r\n\r\nOnce you have an equation, you can solve it and find the unknown value. For example, to solve\u00a0 [latex]20\\%\\cdot{n}=30[\/latex] you can divide [latex]30[\/latex] by [latex]20\\%[\/latex] 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\nWrite an equation that represents the following problem.\r\n<p style=\"text-align: center\">[latex]30[\/latex] is [latex]20\\%[\/latex] 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\">[latex]20\\%[\/latex] of what number is [latex]30[\/latex]?<\/p>\r\nIdentify the percent, the base, and the amount.\r\n\r\nPercent is: \u00a0[latex]20\\%[\/latex]\r\nBase is: unknown\r\nAmount is: [latex]30[\/latex]\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\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate and solve: [latex]36[\/latex] is [latex]\\text{75%}[\/latex] of what number?\r\n[reveal-answer q=\"368537\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"368537\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468657670\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to translate the question '36 is 75% of what number?' Translate the words into an equation, writing 36 as 36, representing the word 'is' with an equals sign, writing 75% as 0.75, representing the word 'of' with a multiplication dot, and letting the variable b be equal to the number. The result is the equation 36 = 0.75 \u00b7 b. Divide both sides of the equation by 0.75. Simplify. The result is 48 = b. 36 is 75% of 48.\">\r\n<tbody>\r\n<tr>\r\n<td>Translate. Let [latex]b=[\/latex] the number.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221918\/CNX_BMath_Figure_06_02_005_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide both sides by [latex]0.75[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{36}{0.75}}={\\Large\\frac{0.75b}{0.75}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]48=b[\/latex]\r\n\r\n[latex]36[\/latex] is [latex]75\\%[\/latex] of [latex]48[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]80098[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\n[latex]\\text{6.5%}[\/latex] of what number is [latex]\\text{\\$1.17}[\/latex]?\r\n[reveal-answer q=\"539196\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"539196\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168466772915\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to translate the question '6.5% of what number is .17?' Translate the words into an equation, writing 6.5% as 0.065, representing the word 'of' with a multiplication dot, letting the variable b be equal to the number, representing the word 'is' with an equals sign, and writing .17 as 1.17. The result is the equation 0.065 \u00b7 n= 1.17. Divide both sides of the equation by 0.065. Simplify. The result is n = 18. 6.5% of 8 is .17.\">\r\n<tbody>\r\n<tr>\r\n<td>Translate. Let [latex]b=[\/latex] the number.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221922\/CNX_BMath_Figure_06_02_006_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide both sides by 0.065.<\/td>\r\n<td>[latex]{\\Large\\frac{0.065n}{0.065}}={\\Large\\frac{1.17}{0.065}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]n=18[\/latex]\r\n\r\n[latex]\\color{blue}{\\text{6.5%}}[\/latex] <span style=\"color: #0000ff\">of<\/span>\u00a0[latex]\\color{blue}{\\text{\\$18}}[\/latex] <span style=\"color: #0000ff\">is\u00a0<\/span>[latex]\\color{blue}{\\text{\\$1.17}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146692[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show another example of how to find the base or whole given percent and amount.\r\n\r\nhttps:\/\/youtu.be\/3etjmUw8K3A\r\n<h2>Solve for the Percent<\/h2>\r\nIn the next examples, we will solve for the percent.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nWhat percent of [latex]72[\/latex] is [latex]9[\/latex]?\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: [latex]72[\/latex]\r\nAmount: [latex]9[\/latex]\r\n\r\nWrite the percent equation: Percent [latex]\\cdot[\/latex] Base = Amount. Use\u00a0[latex]n[\/latex] for the unknown (percent).\r\n<p style=\"text-align: center\">[latex]n\\cdot72=9[\/latex]<\/p>\r\nDivide to undo the multiplication of\u00a0[latex]n[\/latex] times [latex]72[\/latex].\r\n<p style=\"text-align: center\">[latex]n=\\frac{9}{72}[\/latex]<\/p>\r\nDivide [latex]9[\/latex] by [latex]72[\/latex] to find the value for [latex]n[\/latex], 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\n[latex]12.5\\%[\/latex] of [latex]72[\/latex] is [latex]9[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nYou can estimate to see if the answer is reasonable. Use [latex]10\\%[\/latex] and [latex]20\\%[\/latex], numbers close to [latex]12.5\\%[\/latex], to see if they get you close to the answer.\r\n<p style=\"text-align: center\">[latex]10\\%[\/latex] of [latex]72[\/latex] = [latex]0.1[\/latex] \u00b7 [latex]72[\/latex] = [latex]7.2[\/latex]<\/p>\r\n<p style=\"text-align: center\">[latex]20\\%[\/latex] of [latex]72[\/latex] = [latex]0.2[\/latex] \u00b7 [latex]72[\/latex] = [latex]14.4[\/latex]<\/p>\r\nNotice that [latex]9[\/latex] is between [latex]7.2[\/latex] and [latex]14.4[\/latex], so [latex]12.5\\%[\/latex] is reasonable since it is between \u00a0[latex]10\\%[\/latex] and [latex]20\\%[\/latex].\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWhat percent of [latex]36[\/latex] is [latex]9?[\/latex]\r\n[reveal-answer q=\"553638\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"553638\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168467247493\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to translate the question 'what percent of 36 is 9?' Translate the words into algebra, letting the variable p be equal to the percent, representing the word 'of' with a multiplication dot, writing 36 as 36, representing the word 'is' with an equals sign, and writing 9 as 9. The result is the equation p times 36 is equal to 9. Divide both sides of the equation by 36. Simplify. The result is p is equal to one-fourth. Convert the fraction to decimal form. The result is p is equal to 0.25. Convert the decimal to a percent. The result is p is equal to 25%. 25% of 36 is 9.\">\r\n<tbody>\r\n<tr>\r\n<td>Translate into algebra. Let [latex]p=[\/latex] the percent.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221927\/CNX_BMath_Figure_06_02_007_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide by [latex]36[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{36p}{36}}={\\Large\\frac{9}{36}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]p={\\Large\\frac{1}{4}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert to decimal form.<\/td>\r\n<td>[latex]p=0.25[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert to percent.<\/td>\r\n<td>[latex]p=\\text{25%}[\/latex]\r\n\r\n[latex]\\color{blue}{\\text{25%}}[\/latex] <span style=\"color: #0000ff\">of<\/span>\u00a0[latex]\\color{blue}{36}[\/latex] <span style=\"color: #0000ff\">is\u00a0<\/span>[latex]\\color{blue}{9}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146693[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\n[latex]144[\/latex] is what percent of [latex]96?[\/latex]\r\n[reveal-answer q=\"374470\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"374470\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468323289\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to translate the question '144 is what percent of 96?' The first step is to translate the words into algebra, writing 144 as 144, representing the word 'is' with an equals sign, letting the variable p be equal to the percent, representing the word 'of' with a multiplication dot, and writing 96 as 96. The result is the equation 144 = p \u00b7 96. The second step is to divide both sides of the equation by 96. The third step is to simplify. The result is 1.5 = p. The fourth step is to convert the decimal to a percent. 150% = p. 144 is 150% of 96.\">\r\n<tbody>\r\n<tr>\r\n<td>Translate into algebra. Let [latex]p=[\/latex] the percent.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221933\/CNX_BMath_Figure_06_02_008_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide by [latex]96[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{144}{96}}={\\Large\\frac{96p}{96}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]1.5=p[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert to percent.<\/td>\r\n<td>[latex]150\\%=p[\/latex]\r\n\r\n[latex]\\color{blue}{144}[\/latex] <span style=\"color: #0000ff\">is<\/span> [latex]\\color{blue}{\\text{150%}}[\/latex] <span style=\"color: #0000ff\">of<\/span> [latex]\\color{blue}{96}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146866[\/ohm_question]\r\n\r\n<\/div>\r\nIn the next video we show another example of how to find the percent given amount and the base.\r\n\r\nhttps:\/\/youtu.be\/p2KHHFMhJRs","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Translate and solve basic percent equations<\/li>\n<\/ul>\n<\/div>\n<p>We will solve percent equations by using the methods we used to solve equations with fractions or decimals. In the past, you may have solved percent problems by setting them up as proportions. That was the best method available when you did not have the tools of algebra. Now you can translate word sentences into algebraic equations, and then solve the equations.<\/p>\n<p>Remember, percents are fractions, and just like fractions, when finding a percent (or fraction, or portion) of another amount, you multiply.<\/p>\n<p><a href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/understand-percent\/\">In a previous section, we identified\u00a0three important parts to finding the percent of a whole<\/a>:<\/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<h2>Percent of a Whole<\/h2>\n<p>We can use this equation to help us solve equations that require us to find the percent of a whole.<\/p>\n<p>For example, if we knew a gas tank held [latex]14[\/latex] 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 [latex]14[\/latex]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 \u00a0[latex]25\\%[\/latex] of [latex]14[\/latex] 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 [latex]15[\/latex]% of $[latex]200[\/latex]?<\/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>[latex]15\\%[\/latex] of [latex]\\$200[\/latex] is [latex]\\$30[\/latex]<\/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>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<p>In the next examples, we will find the amount. We must be sure to change the given percent to a decimal when we translate the words into an equation.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>What number is [latex]\\text{35%}[\/latex] of [latex]90?[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168467117646\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to translate the question 'what number is 35% of 90?'. Translate the words into algebra, letting the variable n equal the number, representing the word 'is' with an equals sign, writing 35% as 0.35, representing the word 'of' with a multiplication dot, and writing 90 as 90. The result is the equation, n = 0.35 \u00b7 90. Multiply to find that n = 31.5. 31.5 is 35% of 90.\">\n<tbody>\n<tr>\n<td>Translate into algebra. Let [latex]n=[\/latex] the number.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221911\/CNX_BMath_Figure_06_02_003_img-01-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]n=31.5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]31.5[\/latex] is [latex]35\\text{%}[\/latex] of [latex]90[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm80094\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=80094&theme=oea&iframe_resize_id=ohm80094&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>[latex]\\text{125%}[\/latex] of [latex]28[\/latex] is what number?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q892746\">Show Solution<\/span><\/p>\n<div id=\"q892746\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469855167\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to translate the question '125% of 28 is what number?' Translate the words into algebra, writing 125% as 1.25, representing the word 'of' with a multiplication dot, representing the word 'is' with an equals sign, and letting the variable a equal the number. The result is the equation 1.25 \u00b7 28 = a. Multiply to find that 35 = a. 125% of 28 is 35.\">\n<tbody>\n<tr>\n<td>Translate into algebra. Let [latex]a=[\/latex] the number.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221914\/CNX_BMath_Figure_06_02_004_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]35=a[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]125\\text{%}[\/latex] of [latex]28[\/latex] is [latex]35[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Remember that a percent over [latex]100[\/latex] is a number greater than [latex]1[\/latex]. We found that [latex]\\text{125%}[\/latex] of [latex]28[\/latex] is [latex]35[\/latex], which is greater than [latex]28[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146672\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146672&theme=oea&iframe_resize_id=ohm146672&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The video that follows shows how to use the percent equation to find the amount in a percent equation when the percent is greater than [latex]100\\%[\/latex].<\/p>\n<p>https:\/\/youtu.be\/dO3AaW_c9s0he<\/p>\n<h2>Solve for the Base<\/h2>\n<p>In the next examples, we are asked to find the base.<\/p>\n<p>Once you have an equation, you can solve it and find the unknown value. For example, to solve\u00a0 [latex]20\\%\\cdot{n}=30[\/latex] you can divide [latex]30[\/latex] by [latex]20\\%[\/latex] 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>Write an equation that represents the following problem.<\/p>\n<p style=\"text-align: center\">[latex]30[\/latex] is [latex]20\\%[\/latex] 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\">[latex]20\\%[\/latex] of what number is [latex]30[\/latex]?<\/p>\n<p>Identify the percent, the base, and the amount.<\/p>\n<p>Percent is: \u00a0[latex]20\\%[\/latex]<br \/>\nBase is: unknown<br \/>\nAmount is: [latex]30[\/latex]<\/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>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate and solve: [latex]36[\/latex] is [latex]\\text{75%}[\/latex] of what number?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q368537\">Show Solution<\/span><\/p>\n<div id=\"q368537\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468657670\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to translate the question '36 is 75% of what number?' Translate the words into an equation, writing 36 as 36, representing the word 'is' with an equals sign, writing 75% as 0.75, representing the word 'of' with a multiplication dot, and letting the variable b be equal to the number. The result is the equation 36 = 0.75 \u00b7 b. Divide both sides of the equation by 0.75. Simplify. The result is 48 = b. 36 is 75% of 48.\">\n<tbody>\n<tr>\n<td>Translate. Let [latex]b=[\/latex] the number.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221918\/CNX_BMath_Figure_06_02_005_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by [latex]0.75[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{36}{0.75}}={\\Large\\frac{0.75b}{0.75}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]48=b[\/latex]<\/p>\n<p>[latex]36[\/latex] is [latex]75\\%[\/latex] of [latex]48[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm80098\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=80098&theme=oea&iframe_resize_id=ohm80098&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>[latex]\\text{6.5%}[\/latex] of what number is [latex]\\text{\\$1.17}[\/latex]?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q539196\">Show Solution<\/span><\/p>\n<div id=\"q539196\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168466772915\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to translate the question '6.5% of what number is .17?' Translate the words into an equation, writing 6.5% as 0.065, representing the word 'of' with a multiplication dot, letting the variable b be equal to the number, representing the word 'is' with an equals sign, and writing .17 as 1.17. The result is the equation 0.065 \u00b7 n= 1.17. Divide both sides of the equation by 0.065. Simplify. The result is n = 18. 6.5% of 8 is .17.\">\n<tbody>\n<tr>\n<td>Translate. Let [latex]b=[\/latex] the number.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221922\/CNX_BMath_Figure_06_02_006_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by 0.065.<\/td>\n<td>[latex]{\\Large\\frac{0.065n}{0.065}}={\\Large\\frac{1.17}{0.065}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]n=18[\/latex]<\/p>\n<p>[latex]\\color{blue}{\\text{6.5%}}[\/latex] <span style=\"color: #0000ff\">of<\/span>\u00a0[latex]\\color{blue}{\\text{\\$18}}[\/latex] <span style=\"color: #0000ff\">is\u00a0<\/span>[latex]\\color{blue}{\\text{\\$1.17}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146692\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146692&theme=oea&iframe_resize_id=ohm146692&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show another example of how to find the base or whole given percent and amount.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" 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<h2>Solve for the Percent<\/h2>\n<p>In the next examples, we will solve for the percent.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>What percent of [latex]72[\/latex] is [latex]9[\/latex]?<\/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: [latex]72[\/latex]<br \/>\nAmount: [latex]9[\/latex]<\/p>\n<p>Write the percent equation: Percent [latex]\\cdot[\/latex] Base = Amount. Use\u00a0[latex]n[\/latex] 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\u00a0[latex]n[\/latex] times [latex]72[\/latex].<\/p>\n<p style=\"text-align: center\">[latex]n=\\frac{9}{72}[\/latex]<\/p>\n<p>Divide [latex]9[\/latex] by [latex]72[\/latex] to find the value for [latex]n[\/latex], 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>[latex]12.5\\%[\/latex] of [latex]72[\/latex] is [latex]9[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>You can estimate to see if the answer is reasonable. Use [latex]10\\%[\/latex] and [latex]20\\%[\/latex], numbers close to [latex]12.5\\%[\/latex], to see if they get you close to the answer.<\/p>\n<p style=\"text-align: center\">[latex]10\\%[\/latex] of [latex]72[\/latex] = [latex]0.1[\/latex] \u00b7 [latex]72[\/latex] = [latex]7.2[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]20\\%[\/latex] of [latex]72[\/latex] = [latex]0.2[\/latex] \u00b7 [latex]72[\/latex] = [latex]14.4[\/latex]<\/p>\n<p>Notice that [latex]9[\/latex] is between [latex]7.2[\/latex] and [latex]14.4[\/latex], so [latex]12.5\\%[\/latex] is reasonable since it is between \u00a0[latex]10\\%[\/latex] and [latex]20\\%[\/latex].<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>What percent of [latex]36[\/latex] is [latex]9?[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q553638\">Show Solution<\/span><\/p>\n<div id=\"q553638\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168467247493\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to translate the question 'what percent of 36 is 9?' Translate the words into algebra, letting the variable p be equal to the percent, representing the word 'of' with a multiplication dot, writing 36 as 36, representing the word 'is' with an equals sign, and writing 9 as 9. The result is the equation p times 36 is equal to 9. Divide both sides of the equation by 36. Simplify. The result is p is equal to one-fourth. Convert the fraction to decimal form. The result is p is equal to 0.25. Convert the decimal to a percent. The result is p is equal to 25%. 25% of 36 is 9.\">\n<tbody>\n<tr>\n<td>Translate into algebra. Let [latex]p=[\/latex] the percent.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221927\/CNX_BMath_Figure_06_02_007_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide by [latex]36[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{36p}{36}}={\\Large\\frac{9}{36}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]p={\\Large\\frac{1}{4}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert to decimal form.<\/td>\n<td>[latex]p=0.25[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert to percent.<\/td>\n<td>[latex]p=\\text{25%}[\/latex]<\/p>\n<p>[latex]\\color{blue}{\\text{25%}}[\/latex] <span style=\"color: #0000ff\">of<\/span>\u00a0[latex]\\color{blue}{36}[\/latex] <span style=\"color: #0000ff\">is\u00a0<\/span>[latex]\\color{blue}{9}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146693\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146693&theme=oea&iframe_resize_id=ohm146693&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>[latex]144[\/latex] is what percent of [latex]96?[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q374470\">Show Solution<\/span><\/p>\n<div id=\"q374470\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468323289\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to translate the question '144 is what percent of 96?' The first step is to translate the words into algebra, writing 144 as 144, representing the word 'is' with an equals sign, letting the variable p be equal to the percent, representing the word 'of' with a multiplication dot, and writing 96 as 96. The result is the equation 144 = p \u00b7 96. The second step is to divide both sides of the equation by 96. The third step is to simplify. The result is 1.5 = p. The fourth step is to convert the decimal to a percent. 150% = p. 144 is 150% of 96.\">\n<tbody>\n<tr>\n<td>Translate into algebra. Let [latex]p=[\/latex] the percent.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221933\/CNX_BMath_Figure_06_02_008_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide by [latex]96[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{144}{96}}={\\Large\\frac{96p}{96}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]1.5=p[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert to percent.<\/td>\n<td>[latex]150\\%=p[\/latex]<\/p>\n<p>[latex]\\color{blue}{144}[\/latex] <span style=\"color: #0000ff\">is<\/span> [latex]\\color{blue}{\\text{150%}}[\/latex] <span style=\"color: #0000ff\">of<\/span> [latex]\\color{blue}{96}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146866\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146866&theme=oea&iframe_resize_id=ohm146866&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next video we show another example of how to find the percent given amount and the base.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" 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><\/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-10429\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID: 146672, 146692, 146693, 146866. <strong>Authored by<\/strong>: Alyson Day. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/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>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 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\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":8,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"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\":\"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 a Base or Whole Amount\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/3etjmUw8K3A\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID: 146672, 146692, 146693, 146866\",\"author\":\"Alyson Day\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"}]","CANDELA_OUTCOMES_GUID":"099e7b50d88d4d22bec607bc86049e89, 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