{"id":9014,"date":"2017-05-01T15:01:44","date_gmt":"2017-05-01T15:01:44","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9014"},"modified":"2020-10-22T09:09:51","modified_gmt":"2020-10-22T09:09:51","slug":"applications-of-the-addition-and-subtraction-properties","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/applications-of-the-addition-and-subtraction-properties\/","title":{"raw":"7.2.a - Translating and Solving Word Problems and Applications","rendered":"7.2.a &#8211; Translating and Solving Word Problems and Applications"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Translate word phrases to equations and solve<\/li>\r\n \t<li>Translate and solve applications<\/li>\r\n<\/ul>\r\n<\/div>\r\n<a href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-admin\/post.php?post=9243&amp;action=edit\">In previous chapters, we translated word phrases into equations<\/a>. This skill will help you when you solve word problems. Previously, you translated phrases into expressions, and now we will translate phrases into mathematical equations so we can solve them.\u00a0 But before we get started, let's define some important terminology:\r\n<ul>\r\n \t<li><strong>variables:\u00a0<\/strong>\u00a0Variables are symbols that stand for an unknown quantity, often represented with letters, like [latex]x, y[\/latex], or [latex]z[\/latex].<\/li>\r\n \t<li><strong>coefficient:\u00a0<\/strong>Sometimes a variable is multiplied by a number. This number is called the coefficient of the variable. For example, the coefficient of [latex]3x[\/latex] is [latex]3[\/latex].<\/li>\r\n \t<li><strong>term: <\/strong>A\u00a0single number, or variables and numbers connected by multiplication. For example, [latex]-4, 6x[\/latex], and [latex]x^2[\/latex] are all terms.<\/li>\r\n \t<li><strong>expression: <\/strong>Groups of terms connected by addition and subtraction. For example, [latex]2x^2-5[\/latex] is an expression.<\/li>\r\n \t<li><strong>equation: <\/strong>\u00a0An equation is a mathematical statement that two expressions are equal. An equation will always contain an equal sign with an expression on each side.\u00a0Think of an equal sign as meaning \"the same as\". Some examples of equations are\u00a0[latex]y = mx +b[\/latex], \u00a0[latex]\\frac{3}{4}r = v^{3} - r[\/latex], and \u00a0[latex]2(6-d) + f(3 +k) = \\frac{1}{4}d[\/latex] .<\/li>\r\n<\/ul>\r\nThe following figure shows how coefficients, variables, terms, and expressions all come together to make equations. In the equation [latex]2x-3^2=10x[\/latex], the variable is [latex]x[\/latex], a coefficient is [latex]10[\/latex], a term is [latex]10x[\/latex], and an expression is [latex]2x-3^2[\/latex].\r\n\r\n[caption id=\"attachment_4693\" align=\"aligncenter\" width=\"424\"]<img class=\" wp-image-4693\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/117\/2016\/06\/08214552\/Screen-Shot-2016-06-08-at-2.45.15-PM-300x242.png\" alt=\"Equation made of coefficients, variables, terms, and expressions.\" width=\"424\" height=\"342\" \/> Equation made of coefficients, variables, terms, and expressions.[\/caption]\r\n<h2>Translate Phrases into Equations<\/h2>\r\nThe first step in translating phrases into equations is to look for the word (or words) that translate(s) to the equal sign. The table below\u00a0reminds us of some of the words that translate to the equal sign.\r\n<table id=\"fs-id1460732\" summary=\"A table is shown with two rows. The top row says \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th colspan=\"7\">Equals (=)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>is<\/td>\r\n<td>is equal to<\/td>\r\n<td>is the same as<\/td>\r\n<td>the result is<\/td>\r\n<td>gives<\/td>\r\n<td>was<\/td>\r\n<td>will be<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nLet\u2019s review the steps we used to translate a sentence into an equation.\r\n<div class=\"textbox shaded\">\r\n\r\nTranslate a word sentence to an algebraic equation.\r\n<ol id=\"eip-112\" class=\"stepwise\">\r\n \t<li>Locate the \"equals\" word(s). Translate to an equal sign.<\/li>\r\n \t<li>Translate the words to the left of the \"equals\" word(s) into an algebraic expression.<\/li>\r\n \t<li>Translate the words to the right of the \"equals\" word(s) into an algebraic expression.<\/li>\r\n<\/ol>\r\n<\/div>\r\nIn our first example, we will translate and solve a one-step equation.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nTranslate and solve: five more than [latex]x[\/latex] is equal to [latex]26[\/latex].\r\n\r\nSolution:\r\n<table class=\"unnumbered unstyled\" summary=\"The first line says \">\r\n<tbody>\r\n<tr>\r\n<td>Translate.<\/td>\r\n<td>Five more than [latex]x[\/latex] \u00a0 [latex]\\Rightarrow\\quad{x+5}[\/latex]is equal to \u00a0 [latex]\\Rightarrow\\quad{=}[\/latex]\r\n\r\n[latex]26[\/latex] \u00a0 [latex]\\Rightarrow\\quad{26}[\/latex]\r\n\r\n[latex]x+5=26[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract 5 from both sides.<\/td>\r\n<td>[latex]x+5\\color{red}{-5}=26\\color{red}{-5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]x=21[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check:Is [latex]26[\/latex] five more than [latex]21[\/latex] ?\r\n\r\n[latex]21+5\\stackrel{\\text{?}}{=}26[\/latex]\r\n[latex]26=26\\quad\\checkmark[\/latex]\r\nThe solution checks.<\/td>\r\n<td><\/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\u00a0IT<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141742&amp;theme=oea&amp;iframe_resize_id=mom220[\/embed]\r\n\r\n<\/div>\r\n<h3><\/h3>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nTranslate and solve: The difference of [latex]5p[\/latex] and [latex]4p[\/latex] is [latex]23[\/latex].\r\n<p class=\"p1\">[reveal-answer q=\"190834\"]Show Solution[\/reveal-answer]<\/p>\r\n<p class=\"p1\">[hidden-answer a=\"190834\"]<\/p>\r\nSolution:\r\n<table id=\"eip-id1168468483860\" class=\"unnumbered unstyled\" summary=\"The first line says \">\r\n<tbody>\r\n<tr>\r\n<td>Translate.<\/td>\r\n<td>The difference of [latex]5p[\/latex] and [latex]4p[\/latex] \u00a0 [latex]\\Rightarrow\\quad{5p-4p}[\/latex]is \u00a0 [latex]\\Rightarrow\\quad{=}[\/latex]\r\n\r\n[latex]23[\/latex] \u00a0 [latex]\\Rightarrow\\quad{23}[\/latex]\r\n\r\n[latex]5p-4p=23[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]p=23[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check:[latex]5p-4p=23[\/latex]\r\n\r\n[latex]5(23)-4(23)\\stackrel{?}{=}23[\/latex]\r\n[latex]115-92\\stackrel{?}{=}23[\/latex]\r\n[latex]23=23\\quad\\checkmark[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The solution checks.<\/td>\r\n<td><\/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&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY\u00a0it<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141743&amp;theme=oea&amp;iframe_resize_id=mom2[\/embed]\r\n\r\n<\/div>\r\nWatch this video for more examples of how to translate a phrase into\u00a0an equation, then solve it.\r\n\r\nhttps:\/\/youtu.be\/w-64WyZYAMU\r\n<h2>Translate and Solve Applications<\/h2>\r\nIn most of the application problems we solved earlier, we were able to find the quantity we were looking for by simplifying an algebraic expression. Now we will be using equations to solve application problems. We\u2019ll start by restating the problem in just one sentence, then we'll assign a variable, and then we'll translate the sentence into an equation to solve. When assigning a variable, choose a letter that reminds you of what you are looking for.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nThe Robles family has two dogs, Buster and Chandler. Together, they weigh [latex]71[\/latex] pounds.\r\nChandler weighs [latex]28[\/latex] pounds. How much does Buster weigh?\r\n<p class=\"p1\">[reveal-answer q=\"190676\"]Show Solution[\/reveal-answer]<\/p>\r\n<p class=\"p1\">[hidden-answer a=\"190676\"]<\/p>\r\nSolution:\r\n<div>\r\n<table>\r\n<tbody>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 580px;height: 15px\">Read the problem carefully.<\/td>\r\n<td style=\"width: 298px;height: 15px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 58px\">\r\n<td style=\"width: 580px;height: 58px\">Identify what you are asked to find, and choose a variable to represent it.<\/td>\r\n<td style=\"width: 298px;height: 58px\">How much does Buster weigh?Let [latex]b=[\/latex] Buster's weight<\/td>\r\n<\/tr>\r\n<tr style=\"height: 30px\">\r\n<td style=\"width: 580px;height: 30px\">Write a sentence that gives the information to find it.<\/td>\r\n<td style=\"width: 298px;height: 30px\">Buster's weight plus Chandler's weight equals 71 pounds.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 580px;height: 15px\">We will restate the problem, and then include the given information.<\/td>\r\n<td style=\"width: 298px;height: 15px\">Buster's weight plus 28 equals 71.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 580px;height: 15px\">Translate the sentence into an equation, using the variable [latex]b[\/latex].<\/td>\r\n<td style=\"width: 298px;height: 15px\">[latex]b+28=71[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 58px\">\r\n<td style=\"width: 580px;height: 58px\">Solve the equation using good algebraic techniques.<\/td>\r\n<td style=\"width: 298px;height: 58px\">[latex]b+28-28=71-28[\/latex][latex]b=43[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 580px;height: 15px\">Check the answer in the problem and make sure it makes sense.<\/td>\r\n<td style=\"width: 298px;height: 15px\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 580px;height: 15px\">Is 43 pounds a reasonable weight for a dog?<\/td>\r\n<td style=\"width: 298px;height: 15px\">\u00a0Yes.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 580px;height: 15px\">Does Buster's weight plus Chandler's weight equal 71 pounds?<\/td>\r\n<td style=\"width: 298px;height: 15px\">\u00a0[latex]43+28\\stackrel{?}{=}71[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 580px;height: 15px\"><\/td>\r\n<td style=\"width: 298px;height: 15px\">\u00a0[latex]71=71\\quad\\checkmark[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15.0156px\">\r\n<td style=\"width: 580px;height: 15.0156px\">Write a complete sentence that answers the question, \"How much does Buster weigh?\"<\/td>\r\n<td style=\"width: 298px;height: 15.0156px\">Buster weighs [latex]43[\/latex] pounds.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p class=\"p1\">[\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try\u00a0it<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145529&amp;theme=oea&amp;iframe_resize_id=mom520[\/embed]\r\n\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145530&amp;theme=oea&amp;iframe_resize_id=mom550[\/embed]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox shaded\">\r\n<h3 class=\"title\">Devise a problem-solving strategy.<\/h3>\r\n<ol id=\"eip-id1168469608282\" class=\"stepwise\">\r\n \t<li>Read the problem. Make sure you understand all the words and ideas.<\/li>\r\n \t<li>Identify what you are looking for.<\/li>\r\n \t<li>Name what you are looking for. Choose a variable to represent that quantity.<\/li>\r\n \t<li>Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.<\/li>\r\n \t<li>Solve the equation using good algebra techniques.<\/li>\r\n \t<li>Check the answer in the problem and make sure it makes sense.<\/li>\r\n \t<li>Answer the question with a complete sentence.<\/li>\r\n<\/ol>\r\n<\/div>\r\nLet's take a look at the problem-solving strategy in action.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nShayla paid $[latex]24,575[\/latex] for her new car. This was $[latex]875[\/latex] less than the sticker price. What was the sticker price of the car?\r\n<p class=\"p1\">[reveal-answer q=\"210835\"]Show Solution[\/reveal-answer]<\/p>\r\n<p class=\"p1\">[hidden-answer a=\"210835\"]<\/p>\r\nSolution:\r\n<table>\r\n<tbody>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">What are you asked to find?<\/td>\r\n<td style=\"height: 15px\">\"What was the sticker price of the car?\"<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">Assign a variable.<\/td>\r\n<td style=\"height: 15px\">Let [latex]s=[\/latex] the sticker price of the car.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 58px\">\r\n<td style=\"height: 58px\">Write a sentence that gives the information to find it.<\/td>\r\n<td style=\"height: 58px\">$24,575 is $875 less than the sticker price.$24,575 is $875 less than [latex]s[\/latex].<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">Translate into an equation.<\/td>\r\n<td style=\"height: 15px\">[latex]24,575=s-875[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 58px\">\r\n<td style=\"height: 58px\">Solve.<\/td>\r\n<td style=\"height: 58px\">[latex]24,575+875=s-875+875[\/latex][latex]24,575=s[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15.2344px\">\r\n<td style=\"height: 15.2344px\">Check:<\/td>\r\n<td style=\"height: 15.2344px\">Is $875 less than $25,450 equal to $24,575?[latex]25,450 - 875\\stackrel{?}{=}24,575[\/latex]\r\n\r\n[latex]24,575=24,575\\quad\\checkmark[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"height: 15px\">Write a sentence that answers the question.<\/td>\r\n<td style=\"height: 15px\">The sticker price was $[latex]25,450[\/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\nNow you can try translating an equation from a statement that represents subtraction.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try\u00a0it<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141746&amp;theme=oea&amp;iframe_resize_id=mom1[\/embed]\r\n\r\n<\/div>\r\nIn the following video, you will see another example of how to translate a phrase into an equation and solve.\r\n\r\nhttps:\/\/youtu.be\/0eUNh_Qkw9A","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Translate word phrases to equations and solve<\/li>\n<li>Translate and solve applications<\/li>\n<\/ul>\n<\/div>\n<p><a href=\"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-admin\/post.php?post=9243&amp;action=edit\">In previous chapters, we translated word phrases into equations<\/a>. This skill will help you when you solve word problems. Previously, you translated phrases into expressions, and now we will translate phrases into mathematical equations so we can solve them.\u00a0 But before we get started, let&#8217;s define some important terminology:<\/p>\n<ul>\n<li><strong>variables:\u00a0<\/strong>\u00a0Variables are symbols that stand for an unknown quantity, often represented with letters, like [latex]x, y[\/latex], or [latex]z[\/latex].<\/li>\n<li><strong>coefficient:\u00a0<\/strong>Sometimes a variable is multiplied by a number. This number is called the coefficient of the variable. For example, the coefficient of [latex]3x[\/latex] is [latex]3[\/latex].<\/li>\n<li><strong>term: <\/strong>A\u00a0single number, or variables and numbers connected by multiplication. For example, [latex]-4, 6x[\/latex], and [latex]x^2[\/latex] are all terms.<\/li>\n<li><strong>expression: <\/strong>Groups of terms connected by addition and subtraction. For example, [latex]2x^2-5[\/latex] is an expression.<\/li>\n<li><strong>equation: <\/strong>\u00a0An equation is a mathematical statement that two expressions are equal. An equation will always contain an equal sign with an expression on each side.\u00a0Think of an equal sign as meaning &#8220;the same as&#8221;. Some examples of equations are\u00a0[latex]y = mx +b[\/latex], \u00a0[latex]\\frac{3}{4}r = v^{3} - r[\/latex], and \u00a0[latex]2(6-d) + f(3 +k) = \\frac{1}{4}d[\/latex] .<\/li>\n<\/ul>\n<p>The following figure shows how coefficients, variables, terms, and expressions all come together to make equations. In the equation [latex]2x-3^2=10x[\/latex], the variable is [latex]x[\/latex], a coefficient is [latex]10[\/latex], a term is [latex]10x[\/latex], and an expression is [latex]2x-3^2[\/latex].<\/p>\n<div id=\"attachment_4693\" style=\"width: 434px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-4693\" class=\"wp-image-4693\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/117\/2016\/06\/08214552\/Screen-Shot-2016-06-08-at-2.45.15-PM-300x242.png\" alt=\"Equation made of coefficients, variables, terms, and expressions.\" width=\"424\" height=\"342\" \/><\/p>\n<p id=\"caption-attachment-4693\" class=\"wp-caption-text\">Equation made of coefficients, variables, terms, and expressions.<\/p>\n<\/div>\n<h2>Translate Phrases into Equations<\/h2>\n<p>The first step in translating phrases into equations is to look for the word (or words) that translate(s) to the equal sign. The table below\u00a0reminds us of some of the words that translate to the equal sign.<\/p>\n<table id=\"fs-id1460732\" summary=\"A table is shown with two rows. The top row says\">\n<thead>\n<tr valign=\"top\">\n<th colspan=\"7\">Equals (=)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>is<\/td>\n<td>is equal to<\/td>\n<td>is the same as<\/td>\n<td>the result is<\/td>\n<td>gives<\/td>\n<td>was<\/td>\n<td>will be<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Let\u2019s review the steps we used to translate a sentence into an equation.<\/p>\n<div class=\"textbox shaded\">\n<p>Translate a word sentence to an algebraic equation.<\/p>\n<ol id=\"eip-112\" class=\"stepwise\">\n<li>Locate the &#8220;equals&#8221; word(s). Translate to an equal sign.<\/li>\n<li>Translate the words to the left of the &#8220;equals&#8221; word(s) into an algebraic expression.<\/li>\n<li>Translate the words to the right of the &#8220;equals&#8221; word(s) into an algebraic expression.<\/li>\n<\/ol>\n<\/div>\n<p>In our first example, we will translate and solve a one-step equation.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Translate and solve: five more than [latex]x[\/latex] is equal to [latex]26[\/latex].<\/p>\n<p>Solution:<\/p>\n<table class=\"unnumbered unstyled\" summary=\"The first line says\">\n<tbody>\n<tr>\n<td>Translate.<\/td>\n<td>Five more than [latex]x[\/latex] \u00a0 [latex]\\Rightarrow\\quad{x+5}[\/latex]is equal to \u00a0 [latex]\\Rightarrow\\quad{=}[\/latex]<\/p>\n<p>[latex]26[\/latex] \u00a0 [latex]\\Rightarrow\\quad{26}[\/latex]<\/p>\n<p>[latex]x+5=26[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract 5 from both sides.<\/td>\n<td>[latex]x+5\\color{red}{-5}=26\\color{red}{-5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]x=21[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check:Is [latex]26[\/latex] five more than [latex]21[\/latex] ?<\/p>\n<p>[latex]21+5\\stackrel{\\text{?}}{=}26[\/latex]<br \/>\n[latex]26=26\\quad\\checkmark[\/latex]<br \/>\nThe solution checks.<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY\u00a0IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm141742\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141742&#38;theme=oea&#38;iframe_resize_id=ohm141742&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h3><\/h3>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Translate and solve: The difference of [latex]5p[\/latex] and [latex]4p[\/latex] is [latex]23[\/latex].<\/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 Solution<\/span><\/p>\n<p class=\"p1\">\n<div id=\"q190834\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468483860\" class=\"unnumbered unstyled\" summary=\"The first line says\">\n<tbody>\n<tr>\n<td>Translate.<\/td>\n<td>The difference of [latex]5p[\/latex] and [latex]4p[\/latex] \u00a0 [latex]\\Rightarrow\\quad{5p-4p}[\/latex]is \u00a0 [latex]\\Rightarrow\\quad{=}[\/latex]<\/p>\n<p>[latex]23[\/latex] \u00a0 [latex]\\Rightarrow\\quad{23}[\/latex]<\/p>\n<p>[latex]5p-4p=23[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]p=23[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Check:[latex]5p-4p=23[\/latex]<\/p>\n<p>[latex]5(23)-4(23)\\stackrel{?}{=}23[\/latex]<br \/>\n[latex]115-92\\stackrel{?}{=}23[\/latex]<br \/>\n[latex]23=23\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The solution checks.<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p class=\"p1\"><\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY\u00a0it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm141743\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141743&#38;theme=oea&#38;iframe_resize_id=ohm141743&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch this video for more examples of how to translate a phrase into\u00a0an equation, then solve it.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex 1:  Write a Linear Equation in One Variable from a Sentence\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/w-64WyZYAMU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Translate and Solve Applications<\/h2>\n<p>In most of the application problems we solved earlier, we were able to find the quantity we were looking for by simplifying an algebraic expression. Now we will be using equations to solve application problems. We\u2019ll start by restating the problem in just one sentence, then we&#8217;ll assign a variable, and then we&#8217;ll translate the sentence into an equation to solve. When assigning a variable, choose a letter that reminds you of what you are looking for.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>The Robles family has two dogs, Buster and Chandler. Together, they weigh [latex]71[\/latex] pounds.<br \/>\nChandler weighs [latex]28[\/latex] pounds. How much does Buster weigh?<\/p>\n<p class=\"p1\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q190676\">Show Solution<\/span><\/p>\n<p class=\"p1\">\n<div id=\"q190676\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<div>\n<table>\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"width: 580px;height: 15px\">Read the problem carefully.<\/td>\n<td style=\"width: 298px;height: 15px\"><\/td>\n<\/tr>\n<tr style=\"height: 58px\">\n<td style=\"width: 580px;height: 58px\">Identify what you are asked to find, and choose a variable to represent it.<\/td>\n<td style=\"width: 298px;height: 58px\">How much does Buster weigh?Let [latex]b=[\/latex] Buster&#8217;s weight<\/td>\n<\/tr>\n<tr style=\"height: 30px\">\n<td style=\"width: 580px;height: 30px\">Write a sentence that gives the information to find it.<\/td>\n<td style=\"width: 298px;height: 30px\">Buster&#8217;s weight plus Chandler&#8217;s weight equals 71 pounds.<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 580px;height: 15px\">We will restate the problem, and then include the given information.<\/td>\n<td style=\"width: 298px;height: 15px\">Buster&#8217;s weight plus 28 equals 71.<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 580px;height: 15px\">Translate the sentence into an equation, using the variable [latex]b[\/latex].<\/td>\n<td style=\"width: 298px;height: 15px\">[latex]b+28=71[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 58px\">\n<td style=\"width: 580px;height: 58px\">Solve the equation using good algebraic techniques.<\/td>\n<td style=\"width: 298px;height: 58px\">[latex]b+28-28=71-28[\/latex][latex]b=43[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 580px;height: 15px\">Check the answer in the problem and make sure it makes sense.<\/td>\n<td style=\"width: 298px;height: 15px\"><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 580px;height: 15px\">Is 43 pounds a reasonable weight for a dog?<\/td>\n<td style=\"width: 298px;height: 15px\">\u00a0Yes.<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 580px;height: 15px\">Does Buster&#8217;s weight plus Chandler&#8217;s weight equal 71 pounds?<\/td>\n<td style=\"width: 298px;height: 15px\">\u00a0[latex]43+28\\stackrel{?}{=}71[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 580px;height: 15px\"><\/td>\n<td style=\"width: 298px;height: 15px\">\u00a0[latex]71=71\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15.0156px\">\n<td style=\"width: 580px;height: 15.0156px\">Write a complete sentence that answers the question, &#8220;How much does Buster weigh?&#8221;<\/td>\n<td style=\"width: 298px;height: 15.0156px\">Buster weighs [latex]43[\/latex] pounds.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p class=\"p1\"><\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try\u00a0it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145529\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145529&#38;theme=oea&#38;iframe_resize_id=ohm145529&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm145530\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145530&#38;theme=oea&#38;iframe_resize_id=ohm145530&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox shaded\">\n<h3 class=\"title\">Devise a problem-solving strategy.<\/h3>\n<ol id=\"eip-id1168469608282\" class=\"stepwise\">\n<li>Read the problem. Make sure you understand all the words and ideas.<\/li>\n<li>Identify what you are looking for.<\/li>\n<li>Name what you are looking for. Choose a variable to represent that quantity.<\/li>\n<li>Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.<\/li>\n<li>Solve the equation using good algebra techniques.<\/li>\n<li>Check the answer in the problem and make sure it makes sense.<\/li>\n<li>Answer the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<p>Let&#8217;s take a look at the problem-solving strategy in action.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Shayla paid $[latex]24,575[\/latex] for her new car. This was $[latex]875[\/latex] less than the sticker price. What was the sticker price of the car?<\/p>\n<p class=\"p1\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q210835\">Show Solution<\/span><\/p>\n<p class=\"p1\">\n<div id=\"q210835\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table>\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">What are you asked to find?<\/td>\n<td style=\"height: 15px\">&#8220;What was the sticker price of the car?&#8221;<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">Assign a variable.<\/td>\n<td style=\"height: 15px\">Let [latex]s=[\/latex] the sticker price of the car.<\/td>\n<\/tr>\n<tr style=\"height: 58px\">\n<td style=\"height: 58px\">Write a sentence that gives the information to find it.<\/td>\n<td style=\"height: 58px\">$24,575 is $875 less than the sticker price.$24,575 is $875 less than [latex]s[\/latex].<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">Translate into an equation.<\/td>\n<td style=\"height: 15px\">[latex]24,575=s-875[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 58px\">\n<td style=\"height: 58px\">Solve.<\/td>\n<td style=\"height: 58px\">[latex]24,575+875=s-875+875[\/latex][latex]24,575=s[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15.2344px\">\n<td style=\"height: 15.2344px\">Check:<\/td>\n<td style=\"height: 15.2344px\">Is $875 less than $25,450 equal to $24,575?[latex]25,450 - 875\\stackrel{?}{=}24,575[\/latex]<\/p>\n<p>[latex]24,575=24,575\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"height: 15px\">Write a sentence that answers the question.<\/td>\n<td style=\"height: 15px\">The sticker price was $[latex]25,450[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p class=\"p1\"><\/div>\n<\/div>\n<\/div>\n<p>Now you can try translating an equation from a statement that represents subtraction.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try\u00a0it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm141746\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141746&#38;theme=oea&#38;iframe_resize_id=ohm141746&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video, you will see another example of how to translate a phrase into an equation and solve.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"One Step Linear Equation in One Variable App: Sticker Price\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/0eUNh_Qkw9A?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-9014\">\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>One Step Linear Equation in One Variable App: Sticker Price. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/0eUNh_Qkw9A\">https:\/\/youtu.be\/0eUNh_Qkw9A<\/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>Question Id 145529, 145530, 141742, 141743, 141746. <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>. <strong>License Terms<\/strong>: IMathAS Community License, CC-BY + GPL<\/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":13,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"One Step Linear Equation in One Variable App: Sticker Price\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/0eUNh_Qkw9A\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question Id 145529, 145530, 141742, 141743, 141746\",\"author\":\"Lumen 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