{"id":4486,"date":"2020-04-13T14:31:25","date_gmt":"2020-04-13T14:31:25","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4486"},"modified":"2021-02-06T00:04:09","modified_gmt":"2021-02-06T00:04:09","slug":"writing-and-solving-percent-proportions","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/writing-and-solving-percent-proportions\/","title":{"raw":"Writing and Solving Percent Proportions","rendered":"Writing and Solving Percent Proportions"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Translate a statement to a proportion<\/li>\r\n \t<li>Solve a percent proportion<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p>Previously, we solved percent equations by applying the properties of equality we have used to solve equations throughout this text. Some people prefer to solve percent equations by using the proportion method. The proportion method for solving percent problems involves a percent proportion. A <strong>percent proportion<\/strong> is an equation where a percent is equal to an equivalent ratio.<\/p>\r\n<p>For example, [latex]\\text{60%}={\\Large\\frac{60}{100}}[\/latex] and we can simplify [latex]{\\Large\\frac{60}{100}}={\\Large\\frac{3}{5}}[\/latex]. Since the equation [latex]{\\Large\\frac{60}{100}}={\\Large\\frac{3}{5}}[\/latex] shows a percent equal to an equivalent ratio, we call it a percent proportion.<\/p>\r\n<p>Using the vocabulary we used earlier:<\/p>\r\n<p style=\"text-align: center\">[latex]{\\Large\\frac{\\text{amount}}{\\text{base}}}={\\Large\\frac{\\text{percent}}{100}}[\/latex]\r\n[latex]{\\Large\\frac{3}{5}}={\\Large\\frac{60}{100}}[\/latex]<\/p>\r\n\r\n<div class=\"textbox shaded\">\r\n<h3>Percent Proportion<\/h3>\r\nThe amount is to the base as the percent is to [latex]100[\/latex].\r\n\r\n[latex]{\\Large\\frac{\\text{amount}}{\\text{base}}}={\\Large\\frac{\\text{percent}}{100}}[\/latex]\r\n\r\n<\/div>\r\nIf we restate the problem in the words of a proportion, it may be easier to set up the proportion:\r\n<p style=\"padding-left: 30px\">The amount is to the base as the percent is to one hundred.<\/p>\r\nWe could also say:\r\n<p style=\"padding-left: 30px\">The amount out of the base is the same as the percent out of one hundred.<\/p>\r\nFirst we will practice translating into a percent proportion. Later, we\u2019ll solve the proportion.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate to a proportion. What number is [latex]\\text{75%}[\/latex] of [latex]90[\/latex]?\r\n\r\nSolution\r\nIf you look for the word \"of\", it may help you identify the base.\r\n<table id=\"eip-id1166828184051\" class=\"unnumbered unstyled\" summary=\"The figure shows the parts of a percent proportion in the question 'What number is 75% of 90?' It shows 'what number' as the amount, 75% as the percent, and 90 as the base.\">\r\n<tbody>\r\n<tr style=\"height: 67px\">\r\n<td style=\"height: 67px\">Identify the parts of the percent proportion.<\/td>\r\n<td style=\"height: 67px\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222217\/CNX_BMath_Figure_06_05_013_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 24px\">\r\n<td style=\"height: 24px\">Restate as a proportion.<\/td>\r\n<td style=\"height: 24px\">What number out of [latex]90[\/latex] is the same as [latex]75[\/latex] out of [latex]100[\/latex]?<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14.7917px\">\r\n<td style=\"height: 14.7917px\">Set up the proportion. Let [latex]n=\\text{number}[\/latex] .<\/td>\r\n<td style=\"height: 14.7917px\">[latex]{\\Large\\frac{n}{90}}={\\Large\\frac{75}{100}}[\/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]146821[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate to a proportion. [latex]19[\/latex] is [latex]\\text{25%}[\/latex] of what number?\r\n[reveal-answer q=\"203357\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"203357\"]\r\n\r\nSolution\r\n<table id=\"eip-id2096152\" class=\"unnumbered unstyled\" summary=\"The figure shows the parts of a percent proportion in the question '19 is 25% of what number?' It shows 19 as the amount, 25% as the percent, and 'what number' as the base.\">\r\n<tbody>\r\n<tr>\r\n<td>Identify the parts of the percent proportion.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222221\/CNX_BMath_Figure_06_05_014-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Restate as a proportion.<\/td>\r\n<td>[latex]19[\/latex] out of what number is the same as [latex]25[\/latex] out of [latex]100[\/latex]?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Set up the proportion. Let [latex]n=\\text{number}[\/latex] .<\/td>\r\n<td>[latex]{\\Large\\frac{19}{n}}={\\Large\\frac{25}{100}}[\/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]146822[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate to a proportion. What percent of [latex]27[\/latex] is [latex]9[\/latex]?\r\n[reveal-answer q=\"688636\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"688636\"]\r\n\r\nSolution\r\n<table id=\"eip-id1166141441606\" class=\"unnumbered unstyled\" summary=\"The figure shows the parts of a percent proportion in the question 'What percent of 27 is 9?' It shows 'what percent' as the percent, 27 as the base, and 9 as the amount.\">\r\n<tbody>\r\n<tr>\r\n<td>Identify the parts of the percent proportion.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222225\/CNX_BMath_Figure_06_05_015_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Restate as a proportion.<\/td>\r\n<td>[latex]9[\/latex] out of [latex]27[\/latex] is the same as what number out of [latex]100[\/latex]?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Set up the proportion. Let [latex]p=\\text{percent}[\/latex] .<\/td>\r\n<td>[latex]{\\Large\\frac{9}{27}}={\\Large\\frac{p}{100}}[\/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]146825[\/ohm_question]\r\n\r\n<\/div>\r\nNow that we have written percent equations as proportions, we are ready to solve the equations.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate and solve using proportions: What number is [latex]\\text{45%}[\/latex] of [latex]80[\/latex]?\r\n[reveal-answer q=\"33946\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"33946\"]\r\n\r\nSolution\r\n<table id=\"eip-id4251535\" class=\"unnumbered unstyled\" summary=\"The figure shows the parts of a percent proportion in the question 'What number is 45% of 80?' It shows 'what number' as the amount, 45% as the percent, and 80 as the base.\">\r\n<tbody>\r\n<tr style=\"height: 54px\">\r\n<td style=\"height: 54px\">Identify the parts of the percent proportion.<\/td>\r\n<td style=\"height: 54px\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222229\/CNX_BMath_Figure_06_05_016_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15.4375px\">\r\n<td style=\"height: 15.4375px\">Restate as a proportion.<\/td>\r\n<td style=\"height: 15.4375px\">What number out of [latex]80[\/latex] is the same as [latex]45[\/latex] out of [latex]100[\/latex]?<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">Set up the proportion. Let [latex]n=[\/latex] number.<\/td>\r\n<td style=\"height: 15px\">[latex]{\\Large\\frac{n}{80}}={\\Large\\frac{45}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">Find the cross products and set them equal.<\/td>\r\n<td style=\"height: 15px\">[latex]100\\cdot{n}=80\\cdot{45}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">Simplify.<\/td>\r\n<td style=\"height: 15px\">[latex]100n=3,600[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">Divide both sides by [latex]100[\/latex].<\/td>\r\n<td style=\"height: 15px\">[latex]{\\Large\\frac{100n}{100}}={\\Large\\frac{3,600}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">Simplify.<\/td>\r\n<td style=\"height: 15px\">[latex]n=36[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">Check if the answer is reasonable.<\/td>\r\n<td style=\"height: 15px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 30px\">\r\n<td style=\"height: 30px\">Yes. [latex]45[\/latex] is a little less than half of [latex]100[\/latex] and [latex]36[\/latex] is a little less than half [latex]80[\/latex].<\/td>\r\n<td style=\"height: 30px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 30px\">\r\n<td style=\"height: 30px\">Write a complete sentence that answers the question.<\/td>\r\n<td style=\"height: 30px\">[latex]36[\/latex] is [latex]45\\text{%}[\/latex]\u00a0of [latex]80[\/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]146828[\/ohm_question]\r\n\r\n<\/div>\r\nThe following video shows a similar example of how to solve a percent proportion.\r\n\r\nhttps:\/\/youtu.be\/cApv0GeF2XM\r\n\r\nIn the next example, the percent is more than [latex]100[\/latex], which is more than one whole. So the unknown number will be more than the base.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate and solve using proportions: [latex]\\text{125%}[\/latex] of [latex]25[\/latex] is what number?\r\n[reveal-answer q=\"577483\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"577483\"]\r\n\r\nSolution\r\n<table id=\"eip-id1165358285731\" class=\"unnumbered unstyled\" summary=\"The figure shows the parts of a percent proportion in the question '125% of 25 is what number?' It shows 125% as the percent, 25 as the base, and 'what number' as the amount.\">\r\n<tbody>\r\n<tr>\r\n<td>Identify the parts of the percent proportion.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222239\/CNX_BMath_Figure_06_05_17_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Restate as a proportion.<\/td>\r\n<td>What number out of [latex]25[\/latex] is the same as [latex]125[\/latex] out of [latex]100[\/latex]?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Set up the proportion. Let [latex]n=[\/latex] number.<\/td>\r\n<td>[latex]{\\Large\\frac{n}{25}}={\\Large\\frac{125}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the cross products and set them equal.<\/td>\r\n<td>[latex]100\\cdot{n}=25\\cdot{125}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]100n=3,125[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide both sides by [latex]100[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{100n}{100}}={\\Large\\frac{3,125}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]n=31.25[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check if the answer is reasonable.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Yes. [latex]125[\/latex] is more than [latex]100[\/latex] and [latex]31.25[\/latex] is more than [latex]25[\/latex].<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence that answers the question.<\/td>\r\n<td>[latex]125\\text{%}[\/latex] of [latex]25[\/latex] is [latex]31.25[\/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]146839[\/ohm_question]\r\n\r\n<\/div>\r\nPercents with decimals and money are also used in proportions.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate and solve: [latex]\\text{6.5%}[\/latex] of what number is [latex]\\text{\\$1.56}[\/latex]?\r\n[reveal-answer q=\"975951\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"975951\"]\r\n\r\nSolution\r\n<table id=\"eip-id1166127046328\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Identify the parts of the percent proportion.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222249\/CNX_BMath_Figure_06_05_018_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Restate as a proportion.<\/td>\r\n<td>[latex]\\text{\\$1.56}[\/latex] out of what number is the same as [latex]6.5[\/latex] out of [latex]100[\/latex]?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Set up the proportion. Let [latex]n=[\/latex] number.<\/td>\r\n<td>[latex]{\\Large\\frac{1.56}{n}}={\\Large\\frac{6.5}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the cross products and set them equal.<\/td>\r\n<td>[latex]100\\cdot{1.56}=n\\cdot{6.5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]156=6.5n[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide both sides by [latex]6.5[\/latex] to isolate the variable.<\/td>\r\n<td>[latex]{\\Large\\frac{156}{6.5}}={\\Large\\frac{6.5n}{6.5}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]24=n[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check if the answer is reasonable.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Yes. [latex]6.5\\text{%}[\/latex] is a small amount and [latex]\\text{\\$1.56}[\/latex] is much less than [latex]\\text{\\$24}[\/latex].<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence that answers the question.<\/td>\r\n<td>[latex]6.5\\text{%}[\/latex] of [latex]\\text{\\$24}[\/latex] is [latex]\\text{\\$1.56}[\/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]146840[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show a similar problem, note the different wording that results in the same equation.\r\n\r\nhttps:\/\/youtu.be\/wsBhmrmumJo\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate and solve using proportions: What percent of [latex]72[\/latex] is [latex]9?[\/latex]\r\n[reveal-answer q=\"35769\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"35769\"]\r\n\r\nSolution\r\n<table id=\"eip-id1171789006462\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Identify the parts of the percent proportion.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222257\/CNX_BMath_Figure_06_05_019_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Restate as a proportion.<\/td>\r\n<td>[latex]9[\/latex] out of [latex]72[\/latex] is the same as what number out of [latex]100[\/latex]?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Set up the proportion. Let [latex]n=[\/latex] number.<\/td>\r\n<td>[latex]{\\Large\\frac{9}{72}}={\\Large\\frac{n}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the cross products and set them equal.<\/td>\r\n<td>[latex]72\\cdot{n}=100\\cdot{9}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]72n=900[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide both sides by [latex]72[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{72n}{72}}={\\Large\\frac{900}{72}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]n=12.5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check if the answer is reasonable.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Yes. [latex]9[\/latex] is [latex]\\Large\\frac{1}{8}[\/latex] of [latex]72[\/latex], and [latex]\\Large\\frac{1}{8}[\/latex] is [latex]12.5\\text{%}[\/latex].<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence that answers the question.<\/td>\r\n<td>[latex]12.5\\text{%}[\/latex] of [latex]72[\/latex] is [latex]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]146843[\/ohm_question]\r\n\r\n<\/div>\r\nWatch the following video to see a similar problem.\r\n\r\nhttps:\/\/youtu.be\/1GTPRROi1tE","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Translate a statement to a proportion<\/li>\n<li>Solve a percent proportion<\/li>\n<\/ul>\n<\/div>\n<p>Previously, we solved percent equations by applying the properties of equality we have used to solve equations throughout this text. Some people prefer to solve percent equations by using the proportion method. The proportion method for solving percent problems involves a percent proportion. A <strong>percent proportion<\/strong> is an equation where a percent is equal to an equivalent ratio.<\/p>\n<p>For example, [latex]\\text{60%}={\\Large\\frac{60}{100}}[\/latex] and we can simplify [latex]{\\Large\\frac{60}{100}}={\\Large\\frac{3}{5}}[\/latex]. Since the equation [latex]{\\Large\\frac{60}{100}}={\\Large\\frac{3}{5}}[\/latex] shows a percent equal to an equivalent ratio, we call it a percent proportion.<\/p>\n<p>Using the vocabulary we used earlier:<\/p>\n<p style=\"text-align: center\">[latex]{\\Large\\frac{\\text{amount}}{\\text{base}}}={\\Large\\frac{\\text{percent}}{100}}[\/latex]<br \/>\n[latex]{\\Large\\frac{3}{5}}={\\Large\\frac{60}{100}}[\/latex]<\/p>\n<div class=\"textbox shaded\">\n<h3>Percent Proportion<\/h3>\n<p>The amount is to the base as the percent is to [latex]100[\/latex].<\/p>\n<p>[latex]{\\Large\\frac{\\text{amount}}{\\text{base}}}={\\Large\\frac{\\text{percent}}{100}}[\/latex]<\/p>\n<\/div>\n<p>If we restate the problem in the words of a proportion, it may be easier to set up the proportion:<\/p>\n<p style=\"padding-left: 30px\">The amount is to the base as the percent is to one hundred.<\/p>\n<p>We could also say:<\/p>\n<p style=\"padding-left: 30px\">The amount out of the base is the same as the percent out of one hundred.<\/p>\n<p>First we will practice translating into a percent proportion. Later, we\u2019ll solve the proportion.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate to a proportion. What number is [latex]\\text{75%}[\/latex] of [latex]90[\/latex]?<\/p>\n<p>Solution<br \/>\nIf you look for the word &#8220;of&#8221;, it may help you identify the base.<\/p>\n<table id=\"eip-id1166828184051\" class=\"unnumbered unstyled\" summary=\"The figure shows the parts of a percent proportion in the question 'What number is 75% of 90?' It shows 'what number' as the amount, 75% as the percent, and 90 as the base.\">\n<tbody>\n<tr style=\"height: 67px\">\n<td style=\"height: 67px\">Identify the parts of the percent proportion.<\/td>\n<td style=\"height: 67px\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222217\/CNX_BMath_Figure_06_05_013_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr style=\"height: 24px\">\n<td style=\"height: 24px\">Restate as a proportion.<\/td>\n<td style=\"height: 24px\">What number out of [latex]90[\/latex] is the same as [latex]75[\/latex] out of [latex]100[\/latex]?<\/td>\n<\/tr>\n<tr style=\"height: 14.7917px\">\n<td style=\"height: 14.7917px\">Set up the proportion. Let [latex]n=\\text{number}[\/latex] .<\/td>\n<td style=\"height: 14.7917px\">[latex]{\\Large\\frac{n}{90}}={\\Large\\frac{75}{100}}[\/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=\"ohm146821\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146821&theme=oea&iframe_resize_id=ohm146821&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>Translate to a proportion. [latex]19[\/latex] is [latex]\\text{25%}[\/latex] of what number?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q203357\">Show Solution<\/span><\/p>\n<div id=\"q203357\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id2096152\" class=\"unnumbered unstyled\" summary=\"The figure shows the parts of a percent proportion in the question '19 is 25% of what number?' It shows 19 as the amount, 25% as the percent, and 'what number' as the base.\">\n<tbody>\n<tr>\n<td>Identify the parts of the percent proportion.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222221\/CNX_BMath_Figure_06_05_014-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Restate as a proportion.<\/td>\n<td>[latex]19[\/latex] out of what number is the same as [latex]25[\/latex] out of [latex]100[\/latex]?<\/td>\n<\/tr>\n<tr>\n<td>Set up the proportion. Let [latex]n=\\text{number}[\/latex] .<\/td>\n<td>[latex]{\\Large\\frac{19}{n}}={\\Large\\frac{25}{100}}[\/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=\"ohm146822\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146822&theme=oea&iframe_resize_id=ohm146822&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>Translate to a proportion. What percent of [latex]27[\/latex] is [latex]9[\/latex]?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q688636\">Show Solution<\/span><\/p>\n<div id=\"q688636\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1166141441606\" class=\"unnumbered unstyled\" summary=\"The figure shows the parts of a percent proportion in the question 'What percent of 27 is 9?' It shows 'what percent' as the percent, 27 as the base, and 9 as the amount.\">\n<tbody>\n<tr>\n<td>Identify the parts of the percent proportion.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222225\/CNX_BMath_Figure_06_05_015_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Restate as a proportion.<\/td>\n<td>[latex]9[\/latex] out of [latex]27[\/latex] is the same as what number out of [latex]100[\/latex]?<\/td>\n<\/tr>\n<tr>\n<td>Set up the proportion. Let [latex]p=\\text{percent}[\/latex] .<\/td>\n<td>[latex]{\\Large\\frac{9}{27}}={\\Large\\frac{p}{100}}[\/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=\"ohm146825\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146825&theme=oea&iframe_resize_id=ohm146825&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Now that we have written percent equations as proportions, we are ready to solve the equations.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate and solve using proportions: What number is [latex]\\text{45%}[\/latex] of [latex]80[\/latex]?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q33946\">Show Solution<\/span><\/p>\n<div id=\"q33946\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id4251535\" class=\"unnumbered unstyled\" summary=\"The figure shows the parts of a percent proportion in the question 'What number is 45% of 80?' It shows 'what number' as the amount, 45% as the percent, and 80 as the base.\">\n<tbody>\n<tr style=\"height: 54px\">\n<td style=\"height: 54px\">Identify the parts of the percent proportion.<\/td>\n<td style=\"height: 54px\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222229\/CNX_BMath_Figure_06_05_016_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15.4375px\">\n<td style=\"height: 15.4375px\">Restate as a proportion.<\/td>\n<td style=\"height: 15.4375px\">What number out of [latex]80[\/latex] is the same as [latex]45[\/latex] out of [latex]100[\/latex]?<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">Set up the proportion. Let [latex]n=[\/latex] number.<\/td>\n<td style=\"height: 15px\">[latex]{\\Large\\frac{n}{80}}={\\Large\\frac{45}{100}}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">Find the cross products and set them equal.<\/td>\n<td style=\"height: 15px\">[latex]100\\cdot{n}=80\\cdot{45}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">Simplify.<\/td>\n<td style=\"height: 15px\">[latex]100n=3,600[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">Divide both sides by [latex]100[\/latex].<\/td>\n<td style=\"height: 15px\">[latex]{\\Large\\frac{100n}{100}}={\\Large\\frac{3,600}{100}}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">Simplify.<\/td>\n<td style=\"height: 15px\">[latex]n=36[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">Check if the answer is reasonable.<\/td>\n<td style=\"height: 15px\"><\/td>\n<\/tr>\n<tr style=\"height: 30px\">\n<td style=\"height: 30px\">Yes. [latex]45[\/latex] is a little less than half of [latex]100[\/latex] and [latex]36[\/latex] is a little less than half [latex]80[\/latex].<\/td>\n<td style=\"height: 30px\"><\/td>\n<\/tr>\n<tr style=\"height: 30px\">\n<td style=\"height: 30px\">Write a complete sentence that answers the question.<\/td>\n<td style=\"height: 30px\">[latex]36[\/latex] is [latex]45\\text{%}[\/latex]\u00a0of [latex]80[\/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=\"ohm146828\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146828&theme=oea&iframe_resize_id=ohm146828&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The following video shows a similar example of how to solve a percent proportion.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Example 1:  Solve a Percent Problem Using a Percent Proportion\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/cApv0GeF2XM?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>In the next example, the percent is more than [latex]100[\/latex], which is more than one whole. So the unknown number will be more than the base.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate and solve using proportions: [latex]\\text{125%}[\/latex] of [latex]25[\/latex] is what number?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q577483\">Show Solution<\/span><\/p>\n<div id=\"q577483\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1165358285731\" class=\"unnumbered unstyled\" summary=\"The figure shows the parts of a percent proportion in the question '125% of 25 is what number?' It shows 125% as the percent, 25 as the base, and 'what number' as the amount.\">\n<tbody>\n<tr>\n<td>Identify the parts of the percent proportion.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222239\/CNX_BMath_Figure_06_05_17_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Restate as a proportion.<\/td>\n<td>What number out of [latex]25[\/latex] is the same as [latex]125[\/latex] out of [latex]100[\/latex]?<\/td>\n<\/tr>\n<tr>\n<td>Set up the proportion. Let [latex]n=[\/latex] number.<\/td>\n<td>[latex]{\\Large\\frac{n}{25}}={\\Large\\frac{125}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Find the cross products and set them equal.<\/td>\n<td>[latex]100\\cdot{n}=25\\cdot{125}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]100n=3,125[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by [latex]100[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{100n}{100}}={\\Large\\frac{3,125}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]n=31.25[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check if the answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. [latex]125[\/latex] is more than [latex]100[\/latex] and [latex]31.25[\/latex] is more than [latex]25[\/latex].<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>[latex]125\\text{%}[\/latex] of [latex]25[\/latex] is [latex]31.25[\/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=\"ohm146839\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146839&theme=oea&iframe_resize_id=ohm146839&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Percents with decimals and money are also used in proportions.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate and solve: [latex]\\text{6.5%}[\/latex] of what number is [latex]\\text{\\$1.56}[\/latex]?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q975951\">Show Solution<\/span><\/p>\n<div id=\"q975951\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1166127046328\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Identify the parts of the percent proportion.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222249\/CNX_BMath_Figure_06_05_018_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Restate as a proportion.<\/td>\n<td>[latex]\\text{\\$1.56}[\/latex] out of what number is the same as [latex]6.5[\/latex] out of [latex]100[\/latex]?<\/td>\n<\/tr>\n<tr>\n<td>Set up the proportion. Let [latex]n=[\/latex] number.<\/td>\n<td>[latex]{\\Large\\frac{1.56}{n}}={\\Large\\frac{6.5}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Find the cross products and set them equal.<\/td>\n<td>[latex]100\\cdot{1.56}=n\\cdot{6.5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]156=6.5n[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by [latex]6.5[\/latex] to isolate the variable.<\/td>\n<td>[latex]{\\Large\\frac{156}{6.5}}={\\Large\\frac{6.5n}{6.5}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]24=n[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check if the answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. [latex]6.5\\text{%}[\/latex] is a small amount and [latex]\\text{\\$1.56}[\/latex] is much less than [latex]\\text{\\$24}[\/latex].<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>[latex]6.5\\text{%}[\/latex] of [latex]\\text{\\$24}[\/latex] is [latex]\\text{\\$1.56}[\/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=\"ohm146840\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146840&theme=oea&iframe_resize_id=ohm146840&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show a similar problem, note the different wording that results in the same equation.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Example 2:  Solve a Percent Problem Using a Percent Proportion\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/wsBhmrmumJo?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate and solve using proportions: 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=\"q35769\">Show Solution<\/span><\/p>\n<div id=\"q35769\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1171789006462\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Identify the parts of the percent proportion.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222257\/CNX_BMath_Figure_06_05_019_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Restate as a proportion.<\/td>\n<td>[latex]9[\/latex] out of [latex]72[\/latex] is the same as what number out of [latex]100[\/latex]?<\/td>\n<\/tr>\n<tr>\n<td>Set up the proportion. Let [latex]n=[\/latex] number.<\/td>\n<td>[latex]{\\Large\\frac{9}{72}}={\\Large\\frac{n}{100}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Find the cross products and set them equal.<\/td>\n<td>[latex]72\\cdot{n}=100\\cdot{9}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]72n=900[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide both sides by [latex]72[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{72n}{72}}={\\Large\\frac{900}{72}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]n=12.5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check if the answer is reasonable.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Yes. [latex]9[\/latex] is [latex]\\Large\\frac{1}{8}[\/latex] of [latex]72[\/latex], and [latex]\\Large\\frac{1}{8}[\/latex] is [latex]12.5\\text{%}[\/latex].<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence that answers the question.<\/td>\n<td>[latex]12.5\\text{%}[\/latex] of [latex]72[\/latex] is [latex]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=\"ohm146843\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146843&theme=oea&iframe_resize_id=ohm146843&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video to see a similar problem.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Example 3:  Determine What Percent One Number is of Another Using a Percent Proportion\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/1GTPRROi1tE?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-4486\">\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 146843, 146840, 146839, 146828. <strong>Authored 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>Example 2: Solve a Percent Problem Using a Percent Proportion. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/wsBhmrmumJo\">https:\/\/youtu.be\/wsBhmrmumJo<\/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>Example 3: Determine What Percent One Number is of Another Using a Percent Proportion. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/1GTPRROi1tE\">https:\/\/youtu.be\/1GTPRROi1tE<\/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\":\"original\",\"description\":\"Question ID 146843, 146840, 146839, 146828\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Example 2: Solve a Percent Problem Using a Percent 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