{"id":10456,"date":"2017-05-26T20:44:09","date_gmt":"2017-05-26T20:44:09","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10456"},"modified":"2024-04-30T16:45:03","modified_gmt":"2024-04-30T16:45:03","slug":"writing-and-solving-percent-proportions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/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>Write percent equations as proportions<\/li>\r\n \t<li>Translate and solve percent proportion equations<\/li>\r\n<\/ul>\r\n<\/div>\r\n<a href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/solving-applications-with-percent\/\">Previously, we solved percent equations by applying the properties of equality<\/a> 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.\r\n\r\nFor 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.\r\n\r\nUsing the vocabulary we used earlier:\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 class=\"alignnone\" 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=\"From the question, &quot;what number is 75 percent of 90?&quot; &quot;what number&quot; is the amount, 75 percent is the percent, and 90 is the base.\" width=\"435\" height=\"66\" \/><\/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 class=\"alignnone\" 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=\"From the question, &quot;19 is 25 percent of what number?&quot;, 19 is the amount, 25 percent is the percent, and what number is the base.\" width=\"432\" height=\"67\" \/><\/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 class=\"alignnone\" 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=\"From the question &quot;what percent of 27 is 9?&quot; what percent is the percent, 27 is the base, and 9 is the amount.\" width=\"422\" height=\"60\" \/><\/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 class=\"alignnone\" 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=\"From the question &quot;what number is 45% of 80?&quot; what number is the amount, 45 percent is the percent, and 80 is the base.\" width=\"436\" height=\"67\" \/><\/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\" style=\"height: 175px;\" 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 style=\"height: 52px;\">\r\n<td style=\"height: 52px; width: 396.656px;\">Identify the parts of the percent proportion.<\/td>\r\n<td style=\"height: 52px; width: 352.656px;\"><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 style=\"height: 23px;\">\r\n<td style=\"height: 23px; width: 396.656px;\">Restate as a proportion.<\/td>\r\n<td style=\"height: 23px; width: 352.656px;\">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 style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 396.656px;\">Set up the proportion. Let [latex]n=[\/latex] number.<\/td>\r\n<td style=\"height: 11px; width: 352.656px;\">[latex]{\\Large\\frac{n}{25}}={\\Large\\frac{125}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 396.656px;\">Find the cross products and set them equal.<\/td>\r\n<td style=\"height: 11px; width: 352.656px;\">[latex]100\\cdot{n}=25\\cdot{125}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 396.656px;\">Simplify.<\/td>\r\n<td style=\"height: 11px; width: 352.656px;\">[latex]100n=3,125[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 396.656px;\">Divide both sides by [latex]100[\/latex].<\/td>\r\n<td style=\"height: 11px; width: 352.656px;\">[latex]{\\Large\\frac{100n}{100}}={\\Large\\frac{3,125}{100}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 396.656px;\">Simplify.<\/td>\r\n<td style=\"height: 11px; width: 352.656px;\">[latex]n=31.25[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 396.656px;\">Check if the answer is reasonable.<\/td>\r\n<td style=\"height: 11px; width: 352.656px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 23px;\">\r\n<td style=\"height: 23px; width: 396.656px;\">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 style=\"height: 23px; width: 352.656px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px; width: 396.656px;\">Write a complete sentence that answers the question.<\/td>\r\n<td style=\"height: 11px; width: 352.656px;\">[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 class=\"alignnone\" 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=\"From the question &quot;6.5 percent of what number is 1.56 dollars?&quot; 6.5 percent is the percent, what number is the base, and 1.56 dollars is the amount.\" width=\"455\" height=\"63\" \/><\/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 class=\"alignnone\" 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=\"From the question, &quot;what percent of 72 is 9?&quot; what percent is the percent, 72 is the base, and 9 is the amount.\" width=\"418\" height=\"61\" \/><\/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>Write percent equations as proportions<\/li>\n<li>Translate and solve percent proportion equations<\/li>\n<\/ul>\n<\/div>\n<p><a href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/solving-applications-with-percent\/\">Previously, we solved percent equations by applying the properties of equality<\/a> 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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"From the question, &quot;what number is 75 percent of 90?&quot; &quot;what number&quot; is the amount, 75 percent is the percent, and 90 is the base.\" width=\"435\" height=\"66\" \/><\/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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"From the question, &quot;19 is 25 percent of what number?&quot;, 19 is the amount, 25 percent is the percent, and what number is the base.\" width=\"432\" height=\"67\" \/><\/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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"From the question &quot;what percent of 27 is 9?&quot; what percent is the percent, 27 is the base, and 9 is the amount.\" width=\"422\" height=\"60\" \/><\/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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"From the question &quot;what number is 45% of 80?&quot; what number is the amount, 45 percent is the percent, and 80 is the base.\" width=\"436\" height=\"67\" \/><\/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\" style=\"height: 175px;\" 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 style=\"height: 52px;\">\n<td style=\"height: 52px; width: 396.656px;\">Identify the parts of the percent proportion.<\/td>\n<td style=\"height: 52px; width: 352.656px;\"><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 style=\"height: 23px;\">\n<td style=\"height: 23px; width: 396.656px;\">Restate as a proportion.<\/td>\n<td style=\"height: 23px; width: 352.656px;\">What number out of [latex]25[\/latex] is the same as [latex]125[\/latex] out of [latex]100[\/latex]?<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 396.656px;\">Set up the proportion. Let [latex]n=[\/latex] number.<\/td>\n<td style=\"height: 11px; width: 352.656px;\">[latex]{\\Large\\frac{n}{25}}={\\Large\\frac{125}{100}}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 396.656px;\">Find the cross products and set them equal.<\/td>\n<td style=\"height: 11px; width: 352.656px;\">[latex]100\\cdot{n}=25\\cdot{125}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 396.656px;\">Simplify.<\/td>\n<td style=\"height: 11px; width: 352.656px;\">[latex]100n=3,125[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 396.656px;\">Divide both sides by [latex]100[\/latex].<\/td>\n<td style=\"height: 11px; width: 352.656px;\">[latex]{\\Large\\frac{100n}{100}}={\\Large\\frac{3,125}{100}}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 396.656px;\">Simplify.<\/td>\n<td style=\"height: 11px; width: 352.656px;\">[latex]n=31.25[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 396.656px;\">Check if the answer is reasonable.<\/td>\n<td style=\"height: 11px; width: 352.656px;\"><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 396.656px;\">Yes. [latex]125[\/latex] is more than [latex]100[\/latex] and [latex]31.25[\/latex] is more than [latex]25[\/latex].<\/td>\n<td style=\"height: 23px; width: 352.656px;\"><\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px; width: 396.656px;\">Write a complete sentence that answers the question.<\/td>\n<td style=\"height: 11px; width: 352.656px;\">[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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"From the question &quot;6.5 percent of what number is 1.56 dollars?&quot; 6.5 percent is the percent, what number is the base, and 1.56 dollars is the amount.\" width=\"455\" height=\"63\" \/><\/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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"From the question, &quot;what percent of 72 is 9?&quot; what percent is the percent, 72 is the base, and 9 is the amount.\" width=\"418\" height=\"61\" \/><\/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-10456\">\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":17533,"menu_order":24,"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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