{"id":4484,"date":"2020-04-13T14:29:39","date_gmt":"2020-04-13T14:29:39","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4484"},"modified":"2021-02-06T00:04:05","modified_gmt":"2021-02-06T00:04:05","slug":"solving-proportions","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/solving-proportions\/","title":{"raw":"Solving Proportions","rendered":"Solving Proportions"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Solve a proportion equation<\/li>\r\n \t<li>Solve a proportion application<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p>To solve a proportion containing a variable, we remember that the proportion is an equation. All of the techniques we have used so far to solve equations still apply. In the next example, we will solve a proportion by multiplying by the Least Common Denominator (LCD) using the Multiplication Property of Equality.<\/p>\r\n\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSolve: [latex]{\\Large\\frac{x}{63}}={\\Large\\frac{4}{7}}[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168468652606\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to finding the cross products of the proportion 17.5 is to 37.5 as 7 is to 15. The cross multiplication shown is 15 times 17.5 = 262.5 and 37.5 times 7 = 262.5.\">\r\n<tbody>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\" colspan=\"2\"><\/td>\r\n<td style=\"height: 15px\">[latex]{\\Large\\frac{x}{63}}={\\Large\\frac{4}{7}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 30px\">\r\n<td style=\"height: 30px\" colspan=\"2\">To isolate [latex]x[\/latex] , multiply both sides by the LCD, [latex]63[\/latex].<\/td>\r\n<td style=\"height: 30px\">[latex]\\color{red}{63}({\\Large\\frac{x}{63}})=\\color{red}{63}({\\Large\\frac{4}{7}})[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 30px\">\r\n<td style=\"height: 30px\" colspan=\"2\">Simplify.<\/td>\r\n<td style=\"height: 30px\">[latex]x={\\Large\\frac{9\\cdot\\color{red}{7}\\cdot4}{\\color{red}{7}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\" colspan=\"2\">Divide the common factors.<\/td>\r\n<td style=\"height: 15px\">[latex]x=36[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 30px\">\r\n<td style=\"height: 30px\">Check: To check our answer, we substitute into the original proportion.<\/td>\r\n<td style=\"height: 30px\"><\/td>\r\n<td style=\"height: 30px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\"><\/td>\r\n<td style=\"height: 15px\">[latex]{\\Large\\frac{x}{63}}={\\Large\\frac{4}{7}}[\/latex]<\/td>\r\n<td style=\"height: 15px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 30px\">\r\n<td style=\"height: 30px\">Substitute [latex]x=\\color{red}{36}[\/latex]<\/td>\r\n<td style=\"height: 30px\">[latex]{\\Large\\frac{\\color{red}{36}}{63}}\\stackrel{?}{=}{\\Large\\frac{4}{7}}[\/latex]<\/td>\r\n<td style=\"height: 30px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 30px\">\r\n<td style=\"height: 30px\">Show common factors.<\/td>\r\n<td style=\"height: 30px\">[latex]{\\Large\\frac{4\\cdot9}{7\\cdot9}}\\stackrel{?}{=}{\\Large\\frac{4}{7}}[\/latex]<\/td>\r\n<td style=\"height: 30px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15.875px\">\r\n<td style=\"height: 15.875px\">Simplify.<\/td>\r\n<td style=\"height: 15.875px\">[latex]{\\Large\\frac{4}{7}}={\\Large\\frac{4}{7}}[\/latex]<\/td>\r\n<td style=\"height: 15.875px\"><\/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]146811[\/ohm_question]\r\n\r\n<\/div>\r\nIn the next video we show another example of how to solve a proportion equation using the LCD.\r\n\r\nhttps:\/\/youtu.be\/pXvzpSU4DyU\r\n\r\nWhen the variable is in a denominator, we\u2019ll use the fact that the cross products of a proportion are equal to solve the proportions.\r\n\r\nWe can find the cross products of the proportion and then set them equal. Then we solve the resulting equation using our familiar techniques.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSolve: [latex]{\\Large\\frac{144}{a}}={\\Large\\frac{9}{4}}[\/latex]\r\n[reveal-answer q=\"841326\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"841326\"]\r\n\r\nSolution\r\nNotice that the variable is in the denominator, so we will solve by finding the cross products and setting them equal.\r\n<table id=\"eip-id1168469872045\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solve the proportion 144 is to a as 9 is to 4 using cross multiplication. It shows how the cross products are found and set equal to one another. The result is 4 times 144 = a times 9. The equation is simplified to 576 = 9 times a. Both sides of the equation is divided by 9. When simplified, the result is 64 = a. The figure shows the steps to checking that a = 64 is the solution to the proportion 144 is to a as 9 is to 4. It shows 64 being substituted for a in the proportion. The proportion becomes 144 is to 64 as 9 is to 4. The common factors in the proportion are shown. The proportion becomes 9 times 16 is to 4 times 16 as 9 is to 4. The proportion is simplified to 9 is to 4 as 9 is to 4. So the solution a = 64 is correct.\">\r\n<tbody>\r\n<tr>\r\n<td colspan=\"2\"><\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222140\/CNX_BMath_Figure_06_02_024_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Find the cross products and set them equal.<\/td>\r\n<td>[latex]4\\cdot144=a\\cdot9[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Simplify.<\/td>\r\n<td>[latex]576=9a[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Divide both sides by [latex]9[\/latex].<\/td>\r\n<td>[latex]{\\Large\\frac{576}{9}}={\\Large\\frac{9a}{9}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\">Simplify.<\/td>\r\n<td>[latex]64=a[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check your answer.<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\Large\\frac{144}{a}}={\\Large\\frac{9}{4}}[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]a=\\color{red}{64}[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{144}{\\color{red}{64}}}\\stackrel{?}{=}{\\Large\\frac{9}{4}}[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Show common factors..<\/td>\r\n<td>[latex]{\\Large\\frac{9\\cdot16}{4\\cdot16}}\\stackrel{?}{=}{\\Large\\frac{9}{4}}[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{\\Large\\frac{9}{4}}={\\Large\\frac{9}{4}}\\quad\\checkmark[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nAnother method to solve this would be to multiply both sides by the LCD, [latex]4a[\/latex]. Try it and verify that you get the same solution.\r\n\r\nThe following video shows an example of how to solve a similar problem by using the LCD.\r\n\r\nhttps:\/\/youtu.be\/zrgLddU8pFU\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146813[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSolve: [latex]{\\Large\\frac{52}{91}}={\\Large\\frac{-4}{y}}[\/latex]\r\n[reveal-answer q=\"761416\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"761416\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469612644\" class=\"unnumbered unstyled\" style=\"width: 808px\" summary=\"The figure shows the steps to solve the proportion 52 is to 91 as -4 is to y using cross multiplication. It shows how the cross products are found and set equal to one another to form the equation y times 52 equals 91 times negative 4. When simplified, the equation becomes 52 times y = negative 364. Both sides of the equation are divided by 52. When simplified, the result is y = negative 7. The figure shows the steps to checking that y = negative 7 is the solution to the proportion 52 to 91 as negative 4 is to y. It shows negative 7 being substituted for y in the proportion. The proportion becomes 52 is to 91 as -4 is to y. The common factors in the proportion are shown. The proportion becomes 13 times 4 is to 13 times 7 as negative 4 is to negative 7. The proportion is simplified to 4 is to 7 as 4 is to 7. So the solution y= negative 7 is correct.\">\r\n<tbody>\r\n<tr style=\"height: 42px\">\r\n<td style=\"height: 42px;width: 488px\" colspan=\"2\">Find the cross products and set them equal.<\/td>\r\n<td style=\"height: 42px;width: 287px\"><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222150\/CNX_BMath_Figure_06_05_026_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 23px\">\r\n<td style=\"height: 23px;width: 488px\" colspan=\"2\"><\/td>\r\n<td style=\"height: 23px;width: 287px\">[latex]y\\cdot52=91(-4)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 24px\">\r\n<td style=\"height: 24px;width: 488px\" colspan=\"2\">Simplify.<\/td>\r\n<td style=\"height: 24px;width: 287px\">[latex]52y=-364[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 43px\">\r\n<td style=\"height: 43px;width: 488px\" colspan=\"2\">Divide both sides by [latex]52[\/latex].<\/td>\r\n<td style=\"height: 43px;width: 287px\">[latex]{\\Large\\frac{52y}{52}}={\\Large\\frac{-364}{52}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 24.3787px\">\r\n<td style=\"height: 24.3787px;width: 488px\" colspan=\"2\">Simplify.<\/td>\r\n<td style=\"height: 24.3787px;width: 287px\">[latex]y=-7[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"height: 14px;width: 141.75px\">Check:<\/td>\r\n<td style=\"height: 14px;width: 346.25px\"><\/td>\r\n<td style=\"height: 14px;width: 287px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 41px\">\r\n<td style=\"height: 41px;width: 141.75px\"><\/td>\r\n<td style=\"height: 41px;width: 346.25px\">[latex]{\\Large\\frac{52}{91}}={\\Large\\frac{-4}{y}}[\/latex]<\/td>\r\n<td style=\"height: 41px;width: 287px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 40px\">\r\n<td style=\"height: 40px;width: 141.75px\">Substitute [latex]y=\\color{red}{-7}[\/latex]<\/td>\r\n<td style=\"height: 40px;width: 346.25px\">[latex]{\\Large\\frac{52}{91}}\\stackrel{?}{=}{\\Large\\frac{-4}{\\color{red}{-7}}}[\/latex]<\/td>\r\n<td style=\"height: 40px;width: 287px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 42px\">\r\n<td style=\"height: 42px;width: 141.75px\">Show common factors.<\/td>\r\n<td style=\"height: 42px;width: 346.25px\">[latex]{\\Large\\frac{13\\cdot4}{13\\cdot4}}\\stackrel{?}{=}{\\Large\\frac{-4}{\\color{red}{-7}}}[\/latex]<\/td>\r\n<td style=\"height: 42px;width: 287px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 42px\">\r\n<td style=\"height: 42px;width: 141.75px\">Simplify.<\/td>\r\n<td style=\"height: 42px;width: 346.25px\">[latex]{\\Large\\frac{4}{7}}={\\Large\\frac{4}{7}}\\quad\\checkmark[\/latex]<\/td>\r\n<td style=\"height: 42px;width: 287px\"><\/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]146814[\/ohm_question]\r\n\r\n<\/div>\r\n<h3>Solve Applications Using Proportions<\/h3>\r\nThe strategy for solving applications that we have used earlier in this chapter, also works for proportions, since proportions are equations. When we set up the proportion, we must make sure the units are correct\u2014the units in the numerators match and the units in the denominators match.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nWhen pediatricians prescribe acetaminophen to children, they prescribe [latex]5[\/latex] milliliters (ml) of acetaminophen for every [latex]25[\/latex] pounds of the child\u2019s weight. If Zoe weighs [latex]80[\/latex] pounds, how many milliliters of acetaminophen will her doctor prescribe?\r\n[reveal-answer q=\"781594\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"781594\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468389749\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Identify what you are asked to find.<\/td>\r\n<td>How many ml of acetaminophen the doctor will prescribe<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Choose a variable to represent it.<\/td>\r\n<td>Let [latex]a=[\/latex] ml of acetaminophen.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence that gives the information to find it.<\/td>\r\n<td>If [latex]5[\/latex] ml is prescribed for every [latex]25[\/latex] pounds, how much will be prescribed for [latex]80[\/latex] pounds?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate into a proportion.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222200\/CNX_BMath_Figure_06_05_001_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute given values\u2014be careful of the units.<\/td>\r\n<td>[latex]{\\Large\\frac{5}{25}}={\\Large\\frac{a}{80}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply both sides by [latex]80[\/latex].<\/td>\r\n<td>[latex]80\\cdot{\\Large\\frac{5}{25}}=80\\cdot{\\Large\\frac{a}{80}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply and show common factors.<\/td>\r\n<td>[latex]{\\Large\\frac{16\\cdot5\\cdot5}{5\\cdot5}}={\\Large\\frac{80a}{80}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]16=a[\/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. Since [latex]80[\/latex] is about [latex]3[\/latex] times [latex]25[\/latex], the medicine should be about [latex]3[\/latex] times [latex]5[\/latex].<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence.<\/td>\r\n<td>The pediatrician would prescribe [latex]16[\/latex] ml of acetaminophen to Zoe.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nYou could also solve this proportion by setting the cross products equal.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146816[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nOne brand of microwave popcorn has [latex]120[\/latex] calories per serving. A whole bag of this popcorn has [latex]3.5[\/latex] servings. How many calories are in a whole bag of this microwave popcorn?\r\n[reveal-answer q=\"459070\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"459070\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168466068741\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Identify what you are asked to find.<\/td>\r\n<td>How many calories are in a whole bag of microwave popcorn?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Choose a variable to represent it.<\/td>\r\n<td>Let [latex]c=[\/latex] number of calories.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence that gives the information to find it.<\/td>\r\n<td>If there are [latex]120[\/latex] calories per serving, how many calories are in a whole bag with [latex]3.5[\/latex] servings?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate into a proportion.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222206\/CNX_BMath_Figure_06_05_002_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute given values.<\/td>\r\n<td>[latex]{\\Large\\frac{120}{1}}={\\Large\\frac{c}{3.5}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply both sides by [latex]3.5[\/latex].<\/td>\r\n<td>[latex](3.5)({\\Large\\frac{120}{1}})=(3.5)({\\Large\\frac{c}{3.5}})[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]420=c[\/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. Since [latex]3.5[\/latex] is between [latex]3[\/latex] and [latex]4[\/latex], the total calories should be between [latex]360 (3\u22c5120)[\/latex] and [latex]480 (4\u22c5120)[\/latex].<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence.<\/td>\r\n<td>The whole bag of microwave popcorn has [latex]420[\/latex] calories.<\/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]146817[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nJosiah went to Mexico for spring break and changed $[latex]325[\/latex] dollars into Mexican pesos. At that time, the exchange rate had $[latex]1[\/latex] U.S. is equal to [latex]12.54[\/latex] Mexican pesos. How many Mexican pesos did he get for his trip?\r\n[reveal-answer q=\"347314\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"347314\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469868734\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Identify what you are asked to find.<\/td>\r\n<td>How many Mexican pesos did Josiah get?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Choose a variable to represent it.<\/td>\r\n<td>Let [latex]p=[\/latex] number of pesos.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a sentence that gives the information to find it.<\/td>\r\n<td>If [latex]\\text{\\$1}[\/latex] U.S. is equal to [latex]12.54[\/latex] Mexican pesos, then [latex]\\text{\\$325}[\/latex] is how many pesos?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate into a proportion.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222211\/CNX_BMath_Figure_06_05_003_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute given values.<\/td>\r\n<td>[latex]{\\Large\\frac{1}{12.54}}={\\Large\\frac{325}{p}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The variable is in the denominator, so find the cross products and set them equal.<\/td>\r\n<td>[latex]p\\cdot{1}=12.54(325)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]c=4,075.5[\/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]\\text{\\$100}[\/latex] would be [latex]\\text{\\$1,254}[\/latex] pesos. [latex]\\text{\\$325}[\/latex] is a little more than [latex]3[\/latex] times this amount.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write a complete sentence.<\/td>\r\n<td>Josiah has [latex]4075.5[\/latex] pesos for his spring break trip.<\/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]146819[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show another example of how to solve an application that involves proportions.\r\n\r\nhttps:\/\/youtu.be\/vnB1mh5X5cA","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Solve a proportion equation<\/li>\n<li>Solve a proportion application<\/li>\n<\/ul>\n<\/div>\n<p>To solve a proportion containing a variable, we remember that the proportion is an equation. All of the techniques we have used so far to solve equations still apply. In the next example, we will solve a proportion by multiplying by the Least Common Denominator (LCD) using the Multiplication Property of Equality.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Solve: [latex]{\\Large\\frac{x}{63}}={\\Large\\frac{4}{7}}[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168468652606\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to finding the cross products of the proportion 17.5 is to 37.5 as 7 is to 15. The cross multiplication shown is 15 times 17.5 = 262.5 and 37.5 times 7 = 262.5.\">\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\" colspan=\"2\"><\/td>\n<td style=\"height: 15px\">[latex]{\\Large\\frac{x}{63}}={\\Large\\frac{4}{7}}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 30px\">\n<td style=\"height: 30px\" colspan=\"2\">To isolate [latex]x[\/latex] , multiply both sides by the LCD, [latex]63[\/latex].<\/td>\n<td style=\"height: 30px\">[latex]\\color{red}{63}({\\Large\\frac{x}{63}})=\\color{red}{63}({\\Large\\frac{4}{7}})[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 30px\">\n<td style=\"height: 30px\" colspan=\"2\">Simplify.<\/td>\n<td style=\"height: 30px\">[latex]x={\\Large\\frac{9\\cdot\\color{red}{7}\\cdot4}{\\color{red}{7}}}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\" colspan=\"2\">Divide the common factors.<\/td>\n<td style=\"height: 15px\">[latex]x=36[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 30px\">\n<td style=\"height: 30px\">Check: To check our answer, we substitute into the original proportion.<\/td>\n<td style=\"height: 30px\"><\/td>\n<td style=\"height: 30px\"><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\"><\/td>\n<td style=\"height: 15px\">[latex]{\\Large\\frac{x}{63}}={\\Large\\frac{4}{7}}[\/latex]<\/td>\n<td style=\"height: 15px\"><\/td>\n<\/tr>\n<tr style=\"height: 30px\">\n<td style=\"height: 30px\">Substitute [latex]x=\\color{red}{36}[\/latex]<\/td>\n<td style=\"height: 30px\">[latex]{\\Large\\frac{\\color{red}{36}}{63}}\\stackrel{?}{=}{\\Large\\frac{4}{7}}[\/latex]<\/td>\n<td style=\"height: 30px\"><\/td>\n<\/tr>\n<tr style=\"height: 30px\">\n<td style=\"height: 30px\">Show common factors.<\/td>\n<td style=\"height: 30px\">[latex]{\\Large\\frac{4\\cdot9}{7\\cdot9}}\\stackrel{?}{=}{\\Large\\frac{4}{7}}[\/latex]<\/td>\n<td style=\"height: 30px\"><\/td>\n<\/tr>\n<tr style=\"height: 15.875px\">\n<td style=\"height: 15.875px\">Simplify.<\/td>\n<td style=\"height: 15.875px\">[latex]{\\Large\\frac{4}{7}}={\\Large\\frac{4}{7}}[\/latex]<\/td>\n<td style=\"height: 15.875px\"><\/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=\"ohm146811\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146811&theme=oea&iframe_resize_id=ohm146811&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next video we show another example of how to solve a proportion equation using the LCD.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex: Solve a Proportion by Clearing Fractions (x\/a=b\/c, Whole Num  Solution)\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/pXvzpSU4DyU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>When the variable is in a denominator, we\u2019ll use the fact that the cross products of a proportion are equal to solve the proportions.<\/p>\n<p>We can find the cross products of the proportion and then set them equal. Then we solve the resulting equation using our familiar techniques.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Solve: [latex]{\\Large\\frac{144}{a}}={\\Large\\frac{9}{4}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q841326\">Show Solution<\/span><\/p>\n<div id=\"q841326\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nNotice that the variable is in the denominator, so we will solve by finding the cross products and setting them equal.<\/p>\n<table id=\"eip-id1168469872045\" class=\"unnumbered unstyled\" summary=\"The figure shows the steps to solve the proportion 144 is to a as 9 is to 4 using cross multiplication. It shows how the cross products are found and set equal to one another. The result is 4 times 144 = a times 9. The equation is simplified to 576 = 9 times a. Both sides of the equation is divided by 9. When simplified, the result is 64 = a. The figure shows the steps to checking that a = 64 is the solution to the proportion 144 is to a as 9 is to 4. It shows 64 being substituted for a in the proportion. The proportion becomes 144 is to 64 as 9 is to 4. The common factors in the proportion are shown. The proportion becomes 9 times 16 is to 4 times 16 as 9 is to 4. The proportion is simplified to 9 is to 4 as 9 is to 4. So the solution a = 64 is correct.\">\n<tbody>\n<tr>\n<td colspan=\"2\"><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222140\/CNX_BMath_Figure_06_02_024_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Find the cross products and set them equal.<\/td>\n<td>[latex]4\\cdot144=a\\cdot9[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td>[latex]576=9a[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Divide both sides by [latex]9[\/latex].<\/td>\n<td>[latex]{\\Large\\frac{576}{9}}={\\Large\\frac{9a}{9}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\">Simplify.<\/td>\n<td>[latex]64=a[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check your answer.<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]{\\Large\\frac{144}{a}}={\\Large\\frac{9}{4}}[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]a=\\color{red}{64}[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{144}{\\color{red}{64}}}\\stackrel{?}{=}{\\Large\\frac{9}{4}}[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Show common factors..<\/td>\n<td>[latex]{\\Large\\frac{9\\cdot16}{4\\cdot16}}\\stackrel{?}{=}{\\Large\\frac{9}{4}}[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{\\Large\\frac{9}{4}}={\\Large\\frac{9}{4}}\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Another method to solve this would be to multiply both sides by the LCD, [latex]4a[\/latex]. Try it and verify that you get the same solution.<\/p>\n<p>The following video shows an example of how to solve a similar problem by using the LCD.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex: Solve a Proportion by Clearing Fractions ((a\/x=b\/c, Fraction Solution)\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/zrgLddU8pFU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146813\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146813&theme=oea&iframe_resize_id=ohm146813&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>Solve: [latex]{\\Large\\frac{52}{91}}={\\Large\\frac{-4}{y}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q761416\">Show Solution<\/span><\/p>\n<div id=\"q761416\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469612644\" class=\"unnumbered unstyled\" style=\"width: 808px\" summary=\"The figure shows the steps to solve the proportion 52 is to 91 as -4 is to y using cross multiplication. It shows how the cross products are found and set equal to one another to form the equation y times 52 equals 91 times negative 4. When simplified, the equation becomes 52 times y = negative 364. Both sides of the equation are divided by 52. When simplified, the result is y = negative 7. The figure shows the steps to checking that y = negative 7 is the solution to the proportion 52 to 91 as negative 4 is to y. It shows negative 7 being substituted for y in the proportion. The proportion becomes 52 is to 91 as -4 is to y. The common factors in the proportion are shown. The proportion becomes 13 times 4 is to 13 times 7 as negative 4 is to negative 7. The proportion is simplified to 4 is to 7 as 4 is to 7. So the solution y= negative 7 is correct.\">\n<tbody>\n<tr style=\"height: 42px\">\n<td style=\"height: 42px;width: 488px\" colspan=\"2\">Find the cross products and set them equal.<\/td>\n<td style=\"height: 42px;width: 287px\"><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222150\/CNX_BMath_Figure_06_05_026_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr style=\"height: 23px\">\n<td style=\"height: 23px;width: 488px\" colspan=\"2\"><\/td>\n<td style=\"height: 23px;width: 287px\">[latex]y\\cdot52=91(-4)[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 24px\">\n<td style=\"height: 24px;width: 488px\" colspan=\"2\">Simplify.<\/td>\n<td style=\"height: 24px;width: 287px\">[latex]52y=-364[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 43px\">\n<td style=\"height: 43px;width: 488px\" colspan=\"2\">Divide both sides by [latex]52[\/latex].<\/td>\n<td style=\"height: 43px;width: 287px\">[latex]{\\Large\\frac{52y}{52}}={\\Large\\frac{-364}{52}}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 24.3787px\">\n<td style=\"height: 24.3787px;width: 488px\" colspan=\"2\">Simplify.<\/td>\n<td style=\"height: 24.3787px;width: 287px\">[latex]y=-7[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"height: 14px;width: 141.75px\">Check:<\/td>\n<td style=\"height: 14px;width: 346.25px\"><\/td>\n<td style=\"height: 14px;width: 287px\"><\/td>\n<\/tr>\n<tr style=\"height: 41px\">\n<td style=\"height: 41px;width: 141.75px\"><\/td>\n<td style=\"height: 41px;width: 346.25px\">[latex]{\\Large\\frac{52}{91}}={\\Large\\frac{-4}{y}}[\/latex]<\/td>\n<td style=\"height: 41px;width: 287px\"><\/td>\n<\/tr>\n<tr style=\"height: 40px\">\n<td style=\"height: 40px;width: 141.75px\">Substitute [latex]y=\\color{red}{-7}[\/latex]<\/td>\n<td style=\"height: 40px;width: 346.25px\">[latex]{\\Large\\frac{52}{91}}\\stackrel{?}{=}{\\Large\\frac{-4}{\\color{red}{-7}}}[\/latex]<\/td>\n<td style=\"height: 40px;width: 287px\"><\/td>\n<\/tr>\n<tr style=\"height: 42px\">\n<td style=\"height: 42px;width: 141.75px\">Show common factors.<\/td>\n<td style=\"height: 42px;width: 346.25px\">[latex]{\\Large\\frac{13\\cdot4}{13\\cdot4}}\\stackrel{?}{=}{\\Large\\frac{-4}{\\color{red}{-7}}}[\/latex]<\/td>\n<td style=\"height: 42px;width: 287px\"><\/td>\n<\/tr>\n<tr style=\"height: 42px\">\n<td style=\"height: 42px;width: 141.75px\">Simplify.<\/td>\n<td style=\"height: 42px;width: 346.25px\">[latex]{\\Large\\frac{4}{7}}={\\Large\\frac{4}{7}}\\quad\\checkmark[\/latex]<\/td>\n<td style=\"height: 42px;width: 287px\"><\/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=\"ohm146814\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146814&theme=oea&iframe_resize_id=ohm146814&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h3>Solve Applications Using Proportions<\/h3>\n<p>The strategy for solving applications that we have used earlier in this chapter, also works for proportions, since proportions are equations. When we set up the proportion, we must make sure the units are correct\u2014the units in the numerators match and the units in the denominators match.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>When pediatricians prescribe acetaminophen to children, they prescribe [latex]5[\/latex] milliliters (ml) of acetaminophen for every [latex]25[\/latex] pounds of the child\u2019s weight. If Zoe weighs [latex]80[\/latex] pounds, how many milliliters of acetaminophen will her doctor prescribe?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q781594\">Show Solution<\/span><\/p>\n<div id=\"q781594\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468389749\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>How many ml of acetaminophen the doctor will prescribe<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]a=[\/latex] ml of acetaminophen.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>If [latex]5[\/latex] ml is prescribed for every [latex]25[\/latex] pounds, how much will be prescribed for [latex]80[\/latex] pounds?<\/td>\n<\/tr>\n<tr>\n<td>Translate into a proportion.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222200\/CNX_BMath_Figure_06_05_001_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Substitute given values\u2014be careful of the units.<\/td>\n<td>[latex]{\\Large\\frac{5}{25}}={\\Large\\frac{a}{80}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by [latex]80[\/latex].<\/td>\n<td>[latex]80\\cdot{\\Large\\frac{5}{25}}=80\\cdot{\\Large\\frac{a}{80}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply and show common factors.<\/td>\n<td>[latex]{\\Large\\frac{16\\cdot5\\cdot5}{5\\cdot5}}={\\Large\\frac{80a}{80}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]16=a[\/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. Since [latex]80[\/latex] is about [latex]3[\/latex] times [latex]25[\/latex], the medicine should be about [latex]3[\/latex] times [latex]5[\/latex].<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence.<\/td>\n<td>The pediatrician would prescribe [latex]16[\/latex] ml of acetaminophen to Zoe.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>You could also solve this proportion by setting the cross products equal.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146816\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146816&theme=oea&iframe_resize_id=ohm146816&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>One brand of microwave popcorn has [latex]120[\/latex] calories per serving. A whole bag of this popcorn has [latex]3.5[\/latex] servings. How many calories are in a whole bag of this microwave popcorn?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q459070\">Show Solution<\/span><\/p>\n<div id=\"q459070\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168466068741\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>How many calories are in a whole bag of microwave popcorn?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]c=[\/latex] number of calories.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>If there are [latex]120[\/latex] calories per serving, how many calories are in a whole bag with [latex]3.5[\/latex] servings?<\/td>\n<\/tr>\n<tr>\n<td>Translate into a proportion.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222206\/CNX_BMath_Figure_06_05_002_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Substitute given values.<\/td>\n<td>[latex]{\\Large\\frac{120}{1}}={\\Large\\frac{c}{3.5}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by [latex]3.5[\/latex].<\/td>\n<td>[latex](3.5)({\\Large\\frac{120}{1}})=(3.5)({\\Large\\frac{c}{3.5}})[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]420=c[\/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. Since [latex]3.5[\/latex] is between [latex]3[\/latex] and [latex]4[\/latex], the total calories should be between [latex]360 (3\u22c5120)[\/latex] and [latex]480 (4\u22c5120)[\/latex].<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence.<\/td>\n<td>The whole bag of microwave popcorn has [latex]420[\/latex] calories.<\/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=\"ohm146817\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146817&theme=oea&iframe_resize_id=ohm146817&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>Josiah went to Mexico for spring break and changed $[latex]325[\/latex] dollars into Mexican pesos. At that time, the exchange rate had $[latex]1[\/latex] U.S. is equal to [latex]12.54[\/latex] Mexican pesos. How many Mexican pesos did he get for his trip?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q347314\">Show Solution<\/span><\/p>\n<div id=\"q347314\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469868734\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Identify what you are asked to find.<\/td>\n<td>How many Mexican pesos did Josiah get?<\/td>\n<\/tr>\n<tr>\n<td>Choose a variable to represent it.<\/td>\n<td>Let [latex]p=[\/latex] number of pesos.<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence that gives the information to find it.<\/td>\n<td>If [latex]\\text{\\$1}[\/latex] U.S. is equal to [latex]12.54[\/latex] Mexican pesos, then [latex]\\text{\\$325}[\/latex] is how many pesos?<\/td>\n<\/tr>\n<tr>\n<td>Translate into a proportion.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24222211\/CNX_BMath_Figure_06_05_003_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Substitute given values.<\/td>\n<td>[latex]{\\Large\\frac{1}{12.54}}={\\Large\\frac{325}{p}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The variable is in the denominator, so find the cross products and set them equal.<\/td>\n<td>[latex]p\\cdot{1}=12.54(325)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]c=4,075.5[\/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]\\text{\\$100}[\/latex] would be [latex]\\text{\\$1,254}[\/latex] pesos. [latex]\\text{\\$325}[\/latex] is a little more than [latex]3[\/latex] times this amount.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a complete sentence.<\/td>\n<td>Josiah has [latex]4075.5[\/latex] pesos for his spring break trip.<\/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=\"ohm146819\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146819&theme=oea&iframe_resize_id=ohm146819&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show another example of how to solve an application that involves proportions.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Examples:  Applications Using Proportions\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/vnB1mh5X5cA?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-4484\">\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 146819, 146818, 146817. <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>Ex: Solve a Proportion by Clearing Fractions (x\/a=b\/c, Whole Num Solution). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/pXvzpSU4DyU\">https:\/\/youtu.be\/pXvzpSU4DyU<\/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>Ex: Solve a Proportion by Clearing Fractions ((a\/x=b\/c, Fraction Solution). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/zrgLddU8pFU\">https:\/\/youtu.be\/zrgLddU8pFU<\/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>Examples: Applications Using Proportions. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/vnB1mh5X5cA\">https:\/\/youtu.be\/vnB1mh5X5cA<\/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":9,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at 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