{"id":371,"date":"2018-04-17T02:33:32","date_gmt":"2018-04-17T02:33:32","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/?post_type=chapter&#038;p=371"},"modified":"2024-04-26T22:05:35","modified_gmt":"2024-04-26T22:05:35","slug":"problem-solving-strategies","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/chapter\/problem-solving-strategies\/","title":{"raw":"Algebraic Problem Solving Strategies","rendered":"Algebraic Problem Solving Strategies"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning outcome<\/h3>\r\n<ul>\r\n \t<li>Use a problem-solving strategy to set up and solve word problems<\/li>\r\n<\/ul>\r\n<\/div>\r\nThe world is full of word problems. How much money do I need to fill the car with gas? How much should I tip the server at a restaurant? How many socks should I pack for vacation? How big a turkey do I need to buy for Thanksgiving dinner, and what time do I need to put it in the oven? If my sister and I buy our mother a present, how much will each of us pay?\r\n\r\n<img class=\"wp-image-835 size-medium alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2985\/2018\/04\/30220245\/gas-pump-300x215.jpg\" alt=\"Man pumping gas into his car while looking at the display where the cost and gallons pumped are displayed.\" width=\"300\" height=\"215\" \/>\r\n\r\nNow that we can solve equations, we are ready to apply our new skills to word problems.\r\n\r\nPreviously, you translated word phrases into algebraic equations using some basic mathematical vocabulary and symbols. Since then you've increased your math vocabulary as you learned about more algebraic procedures. You've also solved some word problems applying math to everyday situations. This method works as long as the situation is familiar to you and the math is not too complicated.\r\n\r\nNow we'll develop a strategy you can use to solve any word problem. This strategy will help you become successful with word problems. We'll demonstrate the strategy as we solve the following problem.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nPete bought a shirt on sale for $[latex]18[\/latex], which is one-half the original price. What was the original price of the shirt?\r\n\r\nSolution:\r\nStep 1. <strong>Read<\/strong> the problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don't understand, look them up in a dictionary or on the Internet.\r\n<ul id=\"fs-id1764631\">\r\n \t<li><em>In this problem, do you understand what is being discussed? Do you understand every word?<\/em><\/li>\r\n<\/ul>\r\nStep 2. <strong>Identify<\/strong> what you are looking for. It's hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!\r\n<ul id=\"fs-id1475126\">\r\n \t<li><em>In this problem, the words \"what was the original price of the shirt\" tell you what you are looking for: the original price of the shirt.<\/em><\/li>\r\n<\/ul>\r\nStep 3. <strong>Name<\/strong> what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.\r\n<ul id=\"fs-id1171505228428\">\r\n \t<li><em>Let [latex]p=[\/latex] the original price of the shirt<\/em><\/li>\r\n<\/ul>\r\nStep 4. <strong>Translate<\/strong> into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223238\/CNX_BMath_Figure_09_01_002_img.png\" alt=\"18 is one half of the original price translates to the equation 18 equals one half times p. 18 equates to itself. The word &quot;is&quot; translates to the equals sign. One half equates to itself. The word &quot;of&quot; correlates to multiplication. The original price can be represented by p.\" width=\"443\" height=\"76\" \/>\r\nStep 5. <strong>Solve<\/strong> the equation using good algebra techniques. Even if you know the answer right away, using algebra will better prepare you to solve problems that do not have obvious answers.\r\n<table id=\"eip-id1168047368619\" class=\"unnumbered unstyled\" summary=\"The top line reads, \">\r\n<tbody>\r\n<tr>\r\n<td>Write the equation.<\/td>\r\n<td>[latex]18=\\Large\\frac{1}{2}p[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply both sides by 2.<\/td>\r\n<td>[latex]\\color{red}{2}\\cdot18=\\color{red}{2}\\cdot\\Large\\frac{1}{2}\\normalsize p[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]36=p[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nStep 6. <strong>Check<\/strong> the answer in the problem and make sure it makes sense.\r\n<ul id=\"fs-id1594085\">\r\n \t<li><em>We found that<\/em> [latex]p=36[\/latex], <em>which means the original price was<\/em> [latex]\\text{\\$36}[\/latex]. <em>Does<\/em> [latex]\\text{\\$36}[\/latex] <em>make sense in the problem? Yes, because<\/em> [latex]18[\/latex] <em>is one-half of<\/em> [latex]36[\/latex], <em>and the shirt was on sale at half the original price.<\/em><\/li>\r\n<\/ul>\r\nStep 7. <strong>Answer<\/strong> the question with a complete sentence.\r\n<ul id=\"fs-id1495941\">\r\n \t<li><em>The problem asked \"What was the original price of the shirt?\" The answer to the question is: \"The original price of the shirt was<\/em> [latex]\\text{\\$36}[\/latex].\"<\/li>\r\n<\/ul>\r\nIf this were a homework exercise, our work might look like this:\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223244\/CNX_BMath_Figure_09_01_022.png\" alt=\"The top line reads, Let p equal the original price. Below that, we have 18 is one-half the original price, which is followed by 18 equals one half p. Multiply both sides by 2 to get 2 times 18 equals 2 times one half p. The equation simplifies to 36 equals p. The next line reads, check. Is 36 dollars a reasonable price for a shirt? Yes. Is 18 dollars one half of 36? Yes. Thus, we can conclude The original price of the shirt was 36 dollars. \" width=\"542\" height=\"319\" \/>\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try it<\/h3>\r\n[ohm_question]142694[\/ohm_question]\r\n\r\n<\/div>\r\nWe list the steps we took to solve the previous example.\r\n<div class=\"textbox shaded\">\r\n<h3 class=\"title\">Problem-Solving Strategy<\/h3>\r\n<ol id=\"eip-id1168469627809\" class=\"stepwise\">\r\n \t<li><strong>Read<\/strong> the word problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don't understand, look them up in a dictionary or on the internet.<\/li>\r\n \t<li><strong>Identify<\/strong> what you are looking for.<\/li>\r\n \t<li><strong>Name<\/strong> what you are looking for. Choose a variable to represent that quantity.<\/li>\r\n \t<li><strong>Translate<\/strong> into an equation. It may be helpful to first restate the problem in one sentence before translating.<\/li>\r\n \t<li><strong>Solve<\/strong> the equation using good algebra techniques.<\/li>\r\n \t<li><strong>Check<\/strong> the answer in the problem. Make sure it makes sense.<\/li>\r\n \t<li><strong>Answer<\/strong> the question with a complete sentence.<\/li>\r\n<\/ol>\r\n<\/div>\r\nLet's use this approach with another example.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nYash brought apples and bananas to a picnic. The number of apples was three more than twice the number of bananas. Yash brought [latex]11[\/latex] apples to the picnic. How many bananas did he bring?\r\n[reveal-answer q=\"15930\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"15930\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168467372660\" class=\"unnumbered unstyled\" summary=\"Step 1 is to read the problem. \">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>How many bananas did he bring?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name<\/strong> what you are looking for.\r\n\r\nChoose a variable to represent the number of bananas.<\/td>\r\n<td>Let [latex]b=\\text{number of bananas}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong> Restate the problem in one sentence with all the important information.\r\n\r\nTranslate into an equation.<\/td>\r\n<td>[latex]11\\enspace\\Rightarrow[\/latex] The number of apples\r\n\r\n[latex]=\\enspace\\Rightarrow[\/latex] was\r\n\r\n[latex]3\\enspace\\Rightarrow[\/latex] three\r\n\r\n[latex]+\\enspace\\Rightarrow[\/latex] more than\r\n\r\n[latex]2b\\enspace\\Rightarrow[\/latex] twice the number of bananas<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td>[latex]11=2b+3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract 3 from each side.<\/td>\r\n<td>[latex]11\\color{red}{-3}=2b+3\\color{red}{-3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]8=2b[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide each side by 2.<\/td>\r\n<td>[latex]\\Large\\frac{8}{\\color{red}{2}}\\normalsize =\\Large\\frac{2b}{\\color{red}{2}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]4=b[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong> First, is our answer reasonable? Yes, bringing four bananas to a picnic seems reasonable. The problem says the number of apples was three more than twice the number of bananas. If there are four bananas, does that make eleven apples? Twice 4 bananas is 8. Three more than 8 is 11.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>Yash brought 4 bananas to the picnic.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try it<\/h3>\r\n<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142722&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"420\"><\/iframe>\r\n\r\n<\/div>\r\nIn the next example, we will apply our Problem-Solving Strategy to applications of percent.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nNga's car insurance premium increased by [latex]\\text{\\$60}[\/latex], which was [latex]\\text{8%}[\/latex] of the original cost. What was the original cost of the premium?\r\n[reveal-answer q=\"662772\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"662772\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168469833028\" class=\"unnumbered unstyled\" style=\"width: 859px;\" summary=\"Step 1 says, \">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 506.783px;\">Step 1. <strong>Read<\/strong> the problem. Remember, if there are words you don't understand, look them up.<\/td>\r\n<td style=\"width: 328.217px;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 506.783px;\">Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td style=\"width: 328.217px;\">the original cost of the premium<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 506.783px;\">Step 3. <strong>Name.<\/strong> Choose a variable to represent the original cost of premium.<\/td>\r\n<td style=\"width: 328.217px;\">Let [latex]c=\\text{the original cost}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 506.783px;\">Step 4. <strong>Translate.<\/strong> Restate as one sentence. Translate into an equation.<\/td>\r\n<td style=\"width: 328.217px;\"><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223257\/CNX_BMath_Figure_09_01_024_img-01.png\" alt=\"60 dollars was 8 percent of the original cost translates to the equation 60 equals 0.08 times c. 60 dollars equates to 60. The word &quot;was&quot; translates to the equals sign. 8 percent equates to 0.08. The word &quot;of&quot; correlates to mulitplication. The original cost can be represented by c.\" width=\"304\" height=\"71\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 506.783px;\">Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td style=\"width: 328.217px;\">[latex]60=0.08c[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 506.783px;\">Divide both sides by [latex]0.08[\/latex].<\/td>\r\n<td style=\"width: 328.217px;\">[latex]\\Large\\frac{60}{\\color{red}{0.08}}\\normalsize =\\Large\\frac{0.08c}{\\color{red}{0.08}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 506.783px;\">Simplify.<\/td>\r\n<td style=\"width: 328.217px;\">[latex]c=750[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 506.783px;\">Step 6. <strong>Check:<\/strong> Is our answer reasonable? Yes, a [latex]\\text{\\$750}[\/latex] premium on auto insurance is reasonable. Now let's check our algebra. Is 8% of 750 equal to [latex]60[\/latex]?\r\n\r\n[latex]750=c[\/latex]\r\n\r\n[latex]0.08(750)=60[\/latex]\r\n\r\n[latex]60=60\\quad\\checkmark[\/latex]<\/td>\r\n<td style=\"width: 328.217px;\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 506.783px;\">Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td style=\"width: 328.217px;\">The original cost of Nga's premium was [latex]\\text{\\$750}[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try it<\/h3>\r\n<iframe id=\"mom3\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142735&amp;theme=oea&amp;iframe_resize_id=mom3\" width=\"100%\" height=\"350\"><\/iframe>\r\n\r\n<iframe id=\"mom4\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142761&amp;theme=oea&amp;iframe_resize_id=mom4\" width=\"100%\" height=\"350\"><\/iframe>\r\n\r\n<\/div>\r\nNow we will translate and solve number problems. In number problems, you are given some clues about one or more numbers, and you use these clues to build an equation. Number problems don't usually arise on an everyday basis, but they provide a good introduction to practicing the Problem-Solving Strategy. Remember to look for clue words such as <em>difference<\/em>, <em>of<\/em>, and <em>and<\/em>.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nThe difference of a number and six is [latex]13[\/latex]. Find the number.\r\n\r\nSolution:\r\n<table id=\"eip-id1168468711054\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem. Do you understand all the words?<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td>the number<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent the number.<\/td>\r\n<td>Let [latex]n=\\text{the number}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong> Restate as one sentence.\r\n\r\nTranslate into an equation.<\/td>\r\n<td>[latex]n-6\\enspace\\Rightarrow[\/latex] The\u00a0difference of a number and 6\r\n\r\n[latex]=\\enspace\\Rightarrow[\/latex] is\r\n\r\n[latex]13\\enspace\\Rightarrow[\/latex] thirteen\r\n\r\n[latex]n-6=13[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.\r\n\r\nAdd 6 to both sides.\r\n\r\nSimplify.<\/td>\r\n<td>[latex]n-6=13[\/latex]\r\n\r\n[latex]n-6\\color{red}{+6}=13\\color{red}{+6}[\/latex]\r\n\r\n[latex]n=19[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong>\r\n\r\nThe difference of [latex]19[\/latex] and [latex]6[\/latex] is [latex]13[\/latex]. It checks.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td>The number is [latex]19[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n&nbsp;\r\n\r\n<iframe id=\"mom50\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142763&amp;theme=oea&amp;iframe_resize_id=mom50\" width=\"100%\" height=\"250\"><\/iframe>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe sum of twice a number and seven is [latex]15[\/latex]. Find the number.\r\n<p class=\"p1\">[reveal-answer q=\"190834\"]Show Answer[\/reveal-answer]<\/p>\r\n<p class=\"p1\">[hidden-answer a=\"190834\"]<\/p>\r\nSolution:\r\n<table id=\"eip-id1168468309891\" class=\"unnumbered unstyled\" summary=\"Step 1 says to read the problem. \">\r\n<tbody>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px;\">Step 1. <strong>Read<\/strong> the problem.<\/td>\r\n<td style=\"height: 14px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px;\">Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\r\n<td style=\"height: 14px;\">the number<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"height: 14px;\">Step 3. <strong>Name.<\/strong> Choose a variable to represent the number.<\/td>\r\n<td style=\"height: 14px;\">Let [latex]n=\\text{the number}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 58px;\">\r\n<td style=\"height: 58px;\">Step 4. <strong>Translate.<\/strong> Restate the problem as one sentence.\r\n\r\nTranslate into an equation.<\/td>\r\n<td style=\"height: 58px;\">[latex]2n\\enspace\\Rightarrow[\/latex] The\u00a0sum of twice a number\r\n\r\n[latex]+\\enspace\\Rightarrow[\/latex] and\r\n\r\n[latex]7\\enspace\\Rightarrow[\/latex] seven\r\n\r\n[latex]=\\enspace\\Rightarrow[\/latex]\u00a0is\r\n\r\n[latex]15\\enspace\\Rightarrow[\/latex]\u00a0fifteen<\/td>\r\n<\/tr>\r\n<tr style=\"height: 21px;\">\r\n<td style=\"height: 21px;\">Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td style=\"height: 21px;\">[latex]2n+7=15[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px;\">\r\n<td style=\"height: 18px;\">Subtract 7 from each side and simplify.<\/td>\r\n<td style=\"height: 18px;\">[latex]2n=8[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 21px;\">\r\n<td style=\"height: 21px;\">Divide each side by 2 and simplify.<\/td>\r\n<td style=\"height: 21px;\">[latex]n=4[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 135px;\">\r\n<td style=\"height: 135px;\">Step 6. <strong>Check:<\/strong> is the sum of twice [latex]4[\/latex] and [latex]7[\/latex] equal to [latex]15[\/latex]?\r\n\r\n[latex]2\\cdot{4}+7=15[\/latex]\r\n\r\n[latex]8+7=15[\/latex]\r\n\r\n[latex]15=15\\quad\\checkmark[\/latex]<\/td>\r\n<td style=\"height: 135px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14.073px;\">\r\n<td style=\"height: 14.073px;\">Step 7. <strong>Answer<\/strong> the question.<\/td>\r\n<td style=\"height: 14.073px;\">The number is [latex]4[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p class=\"p1\">[\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n<iframe id=\"mom60\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142770&amp;theme=oea&amp;iframe_resize_id=mom60\" width=\"100%\" height=\"250\"><\/iframe>\r\n\r\n<\/div>\r\nWatch the following video to see another example of how to solve a number problem.\r\n\r\nhttps:\/\/youtu.be\/izIIqOztUyI","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning outcome<\/h3>\n<ul>\n<li>Use a problem-solving strategy to set up and solve word problems<\/li>\n<\/ul>\n<\/div>\n<p>The world is full of word problems. How much money do I need to fill the car with gas? How much should I tip the server at a restaurant? How many socks should I pack for vacation? How big a turkey do I need to buy for Thanksgiving dinner, and what time do I need to put it in the oven? If my sister and I buy our mother a present, how much will each of us pay?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-835 size-medium alignright\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2985\/2018\/04\/30220245\/gas-pump-300x215.jpg\" alt=\"Man pumping gas into his car while looking at the display where the cost and gallons pumped are displayed.\" width=\"300\" height=\"215\" \/><\/p>\n<p>Now that we can solve equations, we are ready to apply our new skills to word problems.<\/p>\n<p>Previously, you translated word phrases into algebraic equations using some basic mathematical vocabulary and symbols. Since then you&#8217;ve increased your math vocabulary as you learned about more algebraic procedures. You&#8217;ve also solved some word problems applying math to everyday situations. This method works as long as the situation is familiar to you and the math is not too complicated.<\/p>\n<p>Now we&#8217;ll develop a strategy you can use to solve any word problem. This strategy will help you become successful with word problems. We&#8217;ll demonstrate the strategy as we solve the following problem.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Pete bought a shirt on sale for $[latex]18[\/latex], which is one-half the original price. What was the original price of the shirt?<\/p>\n<p>Solution:<br \/>\nStep 1. <strong>Read<\/strong> the problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don&#8217;t understand, look them up in a dictionary or on the Internet.<\/p>\n<ul id=\"fs-id1764631\">\n<li><em>In this problem, do you understand what is being discussed? Do you understand every word?<\/em><\/li>\n<\/ul>\n<p>Step 2. <strong>Identify<\/strong> what you are looking for. It&#8217;s hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!<\/p>\n<ul id=\"fs-id1475126\">\n<li><em>In this problem, the words &#8220;what was the original price of the shirt&#8221; tell you what you are looking for: the original price of the shirt.<\/em><\/li>\n<\/ul>\n<p>Step 3. <strong>Name<\/strong> what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.<\/p>\n<ul id=\"fs-id1171505228428\">\n<li><em>Let [latex]p=[\/latex] the original price of the shirt<\/em><\/li>\n<\/ul>\n<p>Step 4. <strong>Translate<\/strong> into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223238\/CNX_BMath_Figure_09_01_002_img.png\" alt=\"18 is one half of the original price translates to the equation 18 equals one half times p. 18 equates to itself. The word &quot;is&quot; translates to the equals sign. One half equates to itself. The word &quot;of&quot; correlates to multiplication. The original price can be represented by p.\" width=\"443\" height=\"76\" \/><br \/>\nStep 5. <strong>Solve<\/strong> the equation using good algebra techniques. Even if you know the answer right away, using algebra will better prepare you to solve problems that do not have obvious answers.<\/p>\n<table id=\"eip-id1168047368619\" class=\"unnumbered unstyled\" summary=\"The top line reads,\">\n<tbody>\n<tr>\n<td>Write the equation.<\/td>\n<td>[latex]18=\\Large\\frac{1}{2}p[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply both sides by 2.<\/td>\n<td>[latex]\\color{red}{2}\\cdot18=\\color{red}{2}\\cdot\\Large\\frac{1}{2}\\normalsize p[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]36=p[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Step 6. <strong>Check<\/strong> the answer in the problem and make sure it makes sense.<\/p>\n<ul id=\"fs-id1594085\">\n<li><em>We found that<\/em> [latex]p=36[\/latex], <em>which means the original price was<\/em> [latex]\\text{\\$36}[\/latex]. <em>Does<\/em> [latex]\\text{\\$36}[\/latex] <em>make sense in the problem? Yes, because<\/em> [latex]18[\/latex] <em>is one-half of<\/em> [latex]36[\/latex], <em>and the shirt was on sale at half the original price.<\/em><\/li>\n<\/ul>\n<p>Step 7. <strong>Answer<\/strong> the question with a complete sentence.<\/p>\n<ul id=\"fs-id1495941\">\n<li><em>The problem asked &#8220;What was the original price of the shirt?&#8221; The answer to the question is: &#8220;The original price of the shirt was<\/em> [latex]\\text{\\$36}[\/latex].&#8221;<\/li>\n<\/ul>\n<p>If this were a homework exercise, our work might look like this:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223244\/CNX_BMath_Figure_09_01_022.png\" alt=\"The top line reads, Let p equal the original price. Below that, we have 18 is one-half the original price, which is followed by 18 equals one half p. Multiply both sides by 2 to get 2 times 18 equals 2 times one half p. The equation simplifies to 36 equals p. The next line reads, check. Is 36 dollars a reasonable price for a shirt? Yes. Is 18 dollars one half of 36? Yes. Thus, we can conclude The original price of the shirt was 36 dollars.\" width=\"542\" height=\"319\" \/><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm142694\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142694&theme=oea&iframe_resize_id=ohm142694&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>We list the steps we took to solve the previous example.<\/p>\n<div class=\"textbox shaded\">\n<h3 class=\"title\">Problem-Solving Strategy<\/h3>\n<ol id=\"eip-id1168469627809\" class=\"stepwise\">\n<li><strong>Read<\/strong> the word problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don&#8217;t understand, look them up in a dictionary or on the internet.<\/li>\n<li><strong>Identify<\/strong> what you are looking for.<\/li>\n<li><strong>Name<\/strong> what you are looking for. Choose a variable to represent that quantity.<\/li>\n<li><strong>Translate<\/strong> into an equation. It may be helpful to first restate the problem in one sentence before translating.<\/li>\n<li><strong>Solve<\/strong> the equation using good algebra techniques.<\/li>\n<li><strong>Check<\/strong> the answer in the problem. Make sure it makes sense.<\/li>\n<li><strong>Answer<\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<p>Let&#8217;s use this approach with another example.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Yash brought apples and bananas to a picnic. The number of apples was three more than twice the number of bananas. Yash brought [latex]11[\/latex] apples to the picnic. How many bananas did he bring?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q15930\">Show Answer<\/span><\/p>\n<div id=\"q15930\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168467372660\" class=\"unnumbered unstyled\" summary=\"Step 1 is to read the problem.\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>How many bananas did he bring?<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name<\/strong> what you are looking for.<\/p>\n<p>Choose a variable to represent the number of bananas.<\/td>\n<td>Let [latex]b=\\text{number of bananas}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong> Restate the problem in one sentence with all the important information.<\/p>\n<p>Translate into an equation.<\/td>\n<td>[latex]11\\enspace\\Rightarrow[\/latex] The number of apples<\/p>\n<p>[latex]=\\enspace\\Rightarrow[\/latex] was<\/p>\n<p>[latex]3\\enspace\\Rightarrow[\/latex] three<\/p>\n<p>[latex]+\\enspace\\Rightarrow[\/latex] more than<\/p>\n<p>[latex]2b\\enspace\\Rightarrow[\/latex] twice the number of bananas<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td>[latex]11=2b+3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract 3 from each side.<\/td>\n<td>[latex]11\\color{red}{-3}=2b+3\\color{red}{-3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]8=2b[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide each side by 2.<\/td>\n<td>[latex]\\Large\\frac{8}{\\color{red}{2}}\\normalsize =\\Large\\frac{2b}{\\color{red}{2}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]4=b[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong> First, is our answer reasonable? Yes, bringing four bananas to a picnic seems reasonable. The problem says the number of apples was three more than twice the number of bananas. If there are four bananas, does that make eleven apples? Twice 4 bananas is 8. Three more than 8 is 11.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>Yash brought 4 bananas to the picnic.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142722&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"420\"><\/iframe><\/p>\n<\/div>\n<p>In the next example, we will apply our Problem-Solving Strategy to applications of percent.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Nga&#8217;s car insurance premium increased by [latex]\\text{\\$60}[\/latex], which was [latex]\\text{8%}[\/latex] of the original cost. What was the original cost of the premium?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q662772\">Show Answer<\/span><\/p>\n<div id=\"q662772\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168469833028\" class=\"unnumbered unstyled\" style=\"width: 859px;\" summary=\"Step 1 says,\">\n<tbody>\n<tr>\n<td style=\"width: 506.783px;\">Step 1. <strong>Read<\/strong> the problem. Remember, if there are words you don&#8217;t understand, look them up.<\/td>\n<td style=\"width: 328.217px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 506.783px;\">Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td style=\"width: 328.217px;\">the original cost of the premium<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 506.783px;\">Step 3. <strong>Name.<\/strong> Choose a variable to represent the original cost of premium.<\/td>\n<td style=\"width: 328.217px;\">Let [latex]c=\\text{the original cost}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 506.783px;\">Step 4. <strong>Translate.<\/strong> Restate as one sentence. Translate into an equation.<\/td>\n<td style=\"width: 328.217px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24223257\/CNX_BMath_Figure_09_01_024_img-01.png\" alt=\"60 dollars was 8 percent of the original cost translates to the equation 60 equals 0.08 times c. 60 dollars equates to 60. The word &quot;was&quot; translates to the equals sign. 8 percent equates to 0.08. The word &quot;of&quot; correlates to mulitplication. The original cost can be represented by c.\" width=\"304\" height=\"71\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 506.783px;\">Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td style=\"width: 328.217px;\">[latex]60=0.08c[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 506.783px;\">Divide both sides by [latex]0.08[\/latex].<\/td>\n<td style=\"width: 328.217px;\">[latex]\\Large\\frac{60}{\\color{red}{0.08}}\\normalsize =\\Large\\frac{0.08c}{\\color{red}{0.08}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 506.783px;\">Simplify.<\/td>\n<td style=\"width: 328.217px;\">[latex]c=750[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 506.783px;\">Step 6. <strong>Check:<\/strong> Is our answer reasonable? Yes, a [latex]\\text{\\$750}[\/latex] premium on auto insurance is reasonable. Now let&#8217;s check our algebra. Is 8% of 750 equal to [latex]60[\/latex]?<\/p>\n<p>[latex]750=c[\/latex]<\/p>\n<p>[latex]0.08(750)=60[\/latex]<\/p>\n<p>[latex]60=60\\quad\\checkmark[\/latex]<\/td>\n<td style=\"width: 328.217px;\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 506.783px;\">Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td style=\"width: 328.217px;\">The original cost of Nga&#8217;s premium was [latex]\\text{\\$750}[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom3\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142735&amp;theme=oea&amp;iframe_resize_id=mom3\" width=\"100%\" height=\"350\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"mom4\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142761&amp;theme=oea&amp;iframe_resize_id=mom4\" width=\"100%\" height=\"350\"><\/iframe><\/p>\n<\/div>\n<p>Now we will translate and solve number problems. In number problems, you are given some clues about one or more numbers, and you use these clues to build an equation. Number problems don&#8217;t usually arise on an everyday basis, but they provide a good introduction to practicing the Problem-Solving Strategy. Remember to look for clue words such as <em>difference<\/em>, <em>of<\/em>, and <em>and<\/em>.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>The difference of a number and six is [latex]13[\/latex]. Find the number.<\/p>\n<p>Solution:<\/p>\n<table id=\"eip-id1168468711054\" class=\"unnumbered unstyled\" summary=\"Step 1 says,\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem. Do you understand all the words?<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td>the number<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable to represent the number.<\/td>\n<td>Let [latex]n=\\text{the number}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong> Restate as one sentence.<\/p>\n<p>Translate into an equation.<\/td>\n<td>[latex]n-6\\enspace\\Rightarrow[\/latex] The\u00a0difference of a number and 6<\/p>\n<p>[latex]=\\enspace\\Rightarrow[\/latex] is<\/p>\n<p>[latex]13\\enspace\\Rightarrow[\/latex] thirteen<\/p>\n<p>[latex]n-6=13[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/p>\n<p>Add 6 to both sides.<\/p>\n<p>Simplify.<\/td>\n<td>[latex]n-6=13[\/latex]<\/p>\n<p>[latex]n-6\\color{red}{+6}=13\\color{red}{+6}[\/latex]<\/p>\n<p>[latex]n=19[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong><\/p>\n<p>The difference of [latex]19[\/latex] and [latex]6[\/latex] is [latex]13[\/latex]. It checks.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The number is [latex]19[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p>&nbsp;<\/p>\n<p><iframe loading=\"lazy\" id=\"mom50\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142763&amp;theme=oea&amp;iframe_resize_id=mom50\" width=\"100%\" height=\"250\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The sum of twice a number and seven is [latex]15[\/latex]. Find the number.<\/p>\n<p class=\"p1\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q190834\">Show Answer<\/span><\/p>\n<p class=\"p1\">\n<div id=\"q190834\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468309891\" class=\"unnumbered unstyled\" summary=\"Step 1 says to read the problem.\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px;\">Step 1. <strong>Read<\/strong> the problem.<\/td>\n<td style=\"height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px;\">Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td style=\"height: 14px;\">the number<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px;\">Step 3. <strong>Name.<\/strong> Choose a variable to represent the number.<\/td>\n<td style=\"height: 14px;\">Let [latex]n=\\text{the number}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 58px;\">\n<td style=\"height: 58px;\">Step 4. <strong>Translate.<\/strong> Restate the problem as one sentence.<\/p>\n<p>Translate into an equation.<\/td>\n<td style=\"height: 58px;\">[latex]2n\\enspace\\Rightarrow[\/latex] The\u00a0sum of twice a number<\/p>\n<p>[latex]+\\enspace\\Rightarrow[\/latex] and<\/p>\n<p>[latex]7\\enspace\\Rightarrow[\/latex] seven<\/p>\n<p>[latex]=\\enspace\\Rightarrow[\/latex]\u00a0is<\/p>\n<p>[latex]15\\enspace\\Rightarrow[\/latex]\u00a0fifteen<\/td>\n<\/tr>\n<tr style=\"height: 21px;\">\n<td style=\"height: 21px;\">Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td style=\"height: 21px;\">[latex]2n+7=15[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 18px;\">\n<td style=\"height: 18px;\">Subtract 7 from each side and simplify.<\/td>\n<td style=\"height: 18px;\">[latex]2n=8[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 21px;\">\n<td style=\"height: 21px;\">Divide each side by 2 and simplify.<\/td>\n<td style=\"height: 21px;\">[latex]n=4[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 135px;\">\n<td style=\"height: 135px;\">Step 6. <strong>Check:<\/strong> is the sum of twice [latex]4[\/latex] and [latex]7[\/latex] equal to [latex]15[\/latex]?<\/p>\n<p>[latex]2\\cdot{4}+7=15[\/latex]<\/p>\n<p>[latex]8+7=15[\/latex]<\/p>\n<p>[latex]15=15\\quad\\checkmark[\/latex]<\/td>\n<td style=\"height: 135px;\"><\/td>\n<\/tr>\n<tr style=\"height: 14.073px;\">\n<td style=\"height: 14.073px;\">Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td style=\"height: 14.073px;\">The number is [latex]4[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p class=\"p1\"><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom60\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142770&amp;theme=oea&amp;iframe_resize_id=mom60\" width=\"100%\" height=\"250\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video to see another example of how to solve a number problem.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Write and Solve a Linear Equations to Solve a Number Problem (1)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/izIIqOztUyI?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-371\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Man pumping gas. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.edwards.af.mil\/News\/Article\/828917\/driving-on-base-could-make-you-eligible-for-gas-tax-refund\/\">http:\/\/www.edwards.af.mil\/News\/Article\/828917\/driving-on-base-could-make-you-eligible-for-gas-tax-refund\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em><\/li><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":8,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Man pumping 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