{"id":4092,"date":"2020-04-05T21:06:03","date_gmt":"2020-04-05T21:06:03","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4092"},"modified":"2024-06-26T18:03:39","modified_gmt":"2024-06-26T18:03:39","slug":"translating-and-solving-basic-percent-equations","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/translating-and-solving-basic-percent-equations\/","title":{"raw":"Translating and Solving Basic Percent Equations","rendered":"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>Solve percent equations for percent, amount, and base<\/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 as a prealgebra student, you can translate word sentences into algebraic equations, and then solve the equations.\r\n\r\nWe'll look at a common application of percent\u2014tips to a server at a restaurant\u2014to see how to set up a basic percent application.\r\n\r\nWhen Aolani and her friends ate dinner at a restaurant, the bill came to [latex]\\text{\\$80}[\/latex]. They wanted to leave a [latex]\\text{20%}[\/latex] tip. What amount would the tip be?\r\n\r\nTo solve this, we want to find what <em>amount<\/em> is [latex]\\text{20%}[\/latex] of [latex]\\text{\\$80}[\/latex]. The [latex]\\text{\\$80}[\/latex] is called the <em>base<\/em>. The amount of the tip would be [latex]0.20\\left(80\\right)[\/latex], or [latex]\\text{\\$16}[\/latex] See the image below. To find the amount of the tip, we multiplied the percent by the base.\r\n\r\nA [latex]\\text{20%}[\/latex] tip for an [latex]\\text{\\$80}[\/latex] restaurant bill comes out to [latex]\\text{\\$16}[\/latex].\r\n<h2><img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221909\/CNX_BMath_Figure_06_02_001.png\" alt=\"The figure shows a customer copy of a restaurant receipt with the amount of the bill, $80, and the amount of the tip, $16. There is a group of bills totaling $16.\" \/>Solve for Amount<\/h2>\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\nIn the next video we show another example of finding the base given a percent and the amount.\r\n\r\nhttps:\/\/youtu.be\/jTM7ZMvAzsc\r\n<h2>Solve for the Base<\/h2>\r\nIn the next examples, we are asked to find the base.\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=\"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>Solve percent equations for percent, amount, and base<\/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 as a prealgebra student, you can translate word sentences into algebraic equations, and then solve the equations.<\/p>\n<p>We&#8217;ll look at a common application of percent\u2014tips to a server at a restaurant\u2014to see how to set up a basic percent application.<\/p>\n<p>When Aolani and her friends ate dinner at a restaurant, the bill came to [latex]\\text{\\$80}[\/latex]. They wanted to leave a [latex]\\text{20%}[\/latex] tip. What amount would the tip be?<\/p>\n<p>To solve this, we want to find what <em>amount<\/em> is [latex]\\text{20%}[\/latex] of [latex]\\text{\\$80}[\/latex]. The [latex]\\text{\\$80}[\/latex] is called the <em>base<\/em>. The amount of the tip would be [latex]0.20\\left(80\\right)[\/latex], or [latex]\\text{\\$16}[\/latex] See the image below. To find the amount of the tip, we multiplied the percent by the base.<\/p>\n<p>A [latex]\\text{20%}[\/latex] tip for an [latex]\\text{\\$80}[\/latex] restaurant bill comes out to [latex]\\text{\\$16}[\/latex].<\/p>\n<h2><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221909\/CNX_BMath_Figure_06_02_001.png\" alt=\"The figure shows a customer copy of a restaurant receipt with the amount of the bill, $80, and the amount of the tip, $16. There is a group of bills totaling $16.\" \/>Solve for Amount<\/h2>\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>In the next video we show another example of finding the base given a percent and the amount.<\/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<h2>Solve for the Base<\/h2>\n<p>In the next examples, we are asked to find the base.<\/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=\"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-4092\">\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":25777,"menu_order":10,"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":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4092","chapter","type-chapter","status-publish","hentry"],"part":5569,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4092","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4092\/revisions"}],"predecessor-version":[{"id":5582,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4092\/revisions\/5582"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/5569"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4092\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=4092"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=4092"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=4092"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=4092"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}