{"id":9121,"date":"2017-05-02T14:42:40","date_gmt":"2017-05-02T14:42:40","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9121"},"modified":"2024-04-30T21:27:29","modified_gmt":"2024-04-30T21:27:29","slug":"using-a-problem-solving-strategy-to-solve-number-problems","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/using-a-problem-solving-strategy-to-solve-number-problems\/","title":{"raw":"Using a Problem-Solving Strategy to Solve Number Problems","rendered":"Using a Problem-Solving Strategy to Solve Number Problems"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Solve number problems<\/li>\r\n \t<li>Solve consecutive integer problems<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Solving Number Problems<\/h2>\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 thirteen. 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. Translate into an equation.<\/td>\r\n<td>\u00a0[latex]n-6\\enspace\\Rightarrow[\/latex] The difference of a number and 6\r\n[latex]=\\enspace\\Rightarrow[\/latex] is\r\n[latex]13\\enspace\\Rightarrow[\/latex] thirteen<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation. Add 6 to both sides.\r\nSimplify.<\/td>\r\n<td>[latex]n-6=13[\/latex]\r\n[latex]n-6\\color{red}{+6}=13\\color{red}{+6}[\/latex]\r\n[latex]n=19[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong>The 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&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n&nbsp;\r\n\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142763&amp;theme=oea&amp;iframe_resize_id=mom50[\/embed]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe sum of twice a number and seven is fifteen. Find the number.\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-id1168468309891\" class=\"unnumbered unstyled\" summary=\"Step 1 says 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>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 the problem as one sentence.\r\nTranslate into an equation.<\/td>\r\n<td>[latex]2n\\enspace\\Rightarrow[\/latex] The sum of twice a number\r\n[latex]+\\enspace\\Rightarrow[\/latex] and\r\n[latex]7\\enspace\\Rightarrow[\/latex] seven\r\n[latex]=\\enspace\\Rightarrow[\/latex] is\r\n[latex]15\\enspace\\Rightarrow[\/latex] fifteen<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td>[latex]2n+7=15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract 7 from each side and simplify.<\/td>\r\n<td>[latex]2n=8[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide each side by 2 and simplify.<\/td>\r\n<td>[latex]n=4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong> is the sum of twice [latex]4[\/latex] and [latex]7[\/latex] equal to [latex]15[\/latex]?<\/td>\r\n<td>[latex]2\\cdot{4}+7=15[\/latex]\r\n[latex]8+7=15[\/latex]\r\n[latex]15=15\\quad\\checkmark[\/latex]<\/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]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&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142770&amp;theme=oea&amp;iframe_resize_id=mom60[\/embed]\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\r\n<h3>Solving for Two or More Numbers<\/h3>\r\nSome number word problems ask you to find two or more numbers. It may be tempting to name them all with different variables, but so far we have only solved equations with one variable. We will define the numbers in terms of the same variable. Be sure to read the problem carefully to discover how all the numbers relate to each other.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nOne number is five more than another. The sum of the numbers is twenty-one. Find the numbers.\r\n<p class=\"p1\">[reveal-answer q=\"200999\"]Show Solution[\/reveal-answer]<\/p>\r\n<p class=\"p1\">[hidden-answer a=\"200999\"]<\/p>\r\nSolution:\r\n<table id=\"eip-id1168466015145\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem.<\/td>\r\n<td><\/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><\/td>\r\n<td>You are looking for two numbers.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong>Choose a variable to represent the first number.\r\n\r\nWhat do you know about the second number?\r\n\r\nTranslate.<\/td>\r\n<td><\/td>\r\n<td>Let [latex]n=\\text{1st number}[\/latex]One number is five more than another.\r\n\r\n[latex]n+5={2}^{\\text{nd}}\\text{number}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong>Restate the problem as one sentence with all the important information.\r\n\r\nTranslate into an equation.\r\n\r\nSubstitute the variable expressions.<\/td>\r\n<td><\/td>\r\n<td>The sum of the numbers is [latex]21[\/latex].The sum of the 1st number and the 2nd number is [latex]21[\/latex].\r\n\r\n[latex]n\\enspace\\Rightarrow[\/latex]\u00a0First number\r\n\r\n[latex]+\\enspace\\Rightarrow[\/latex] +\r\n\r\n[latex]n+5\\enspace\\Rightarrow[\/latex] Second number\r\n\r\n[latex]=\\enspace\\Rightarrow[\/latex]\u00a0=\r\n\r\n[latex]21\\enspace\\Rightarrow[\/latex]\u00a0twenty-one<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td><\/td>\r\n<td>[latex]n+n+5=21[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td><\/td>\r\n<td>[latex]2n+5=21[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract five from both sides and simplify.<\/td>\r\n<td><\/td>\r\n<td>[latex]2n=16[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide by two and simplify.<\/td>\r\n<td><\/td>\r\n<td>[latex]n=8[\/latex] \u00a0 \u00a0 1st number<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Now find the second number.<\/td>\r\n<td><\/td>\r\n<td>[latex]n+5[\/latex] \u00a0 \u00a0 2nd number<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]n = 8[\/latex]<\/td>\r\n<td><\/td>\r\n<td>[latex]\\color{red}{8}+5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>[latex]13[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Do these numbers check in the problem?Is one number 5 more than the other?\r\n\r\nIs thirteen, 5 more than 8? Yes.\r\n\r\nIs the sum of the two numbers 21?<\/td>\r\n<td>[latex]13\\stackrel{\\text{?}}{=}8+5[\/latex][latex]13=13\\quad\\checkmark[\/latex]\r\n\r\n[latex]8+13\\stackrel{\\text{?}}{=}21[\/latex]\r\n\r\n[latex]21=21\\quad\\checkmark[\/latex]<\/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><\/td>\r\n<td>The numbers are [latex]8[\/latex] and [latex]13[\/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&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n&nbsp;\r\n\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142775&amp;theme=oea&amp;iframe_resize_id=mom70[\/embed]\r\n\r\n<\/div>\r\nWatch the following video to see another example of how to find two numbers given the relationship between the two.\r\n\r\nhttps:\/\/youtu.be\/juslHscrh8s\r\n<h3><\/h3>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe sum of two numbers is negative fourteen. One number is four less than the other. Find the numbers.\r\n<p class=\"p1\">[reveal-answer q=\"500777\"]Show Solution[\/reveal-answer]<\/p>\r\n<p class=\"p1\">[hidden-answer a=\"500777\"]<\/p>\r\nSolution:\r\n<table id=\"eip-id1168469638662\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem.<\/td>\r\n<td><\/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><\/td>\r\n<td>two numbers<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable.What do you know about the second number?\r\n\r\nTranslate.<\/td>\r\n<td><\/td>\r\n<td>Let [latex]n=\\text{1st number}[\/latex]One number is [latex]4[\/latex] less than the other.\r\n\r\n[latex]n-4={2}^{\\text{nd}}\\text{number}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong>Write as one sentence.\r\n\r\nTranslate into an equation.\r\n\r\nSubstitute the variable expressions.<\/td>\r\n<td><\/td>\r\n<td>The sum of two numbers is negative fourteen.[latex]n\\enspace\\Rightarrow[\/latex]\u00a0First number\r\n\r\n[latex]+\\enspace\\Rightarrow[\/latex]\u00a0+\r\n\r\n[latex]n-4\\enspace\\Rightarrow[\/latex] Second number\r\n\r\n[latex]=\\enspace\\Rightarrow[\/latex]\u00a0=\r\n\r\n[latex]-14\\enspace\\Rightarrow[\/latex]\u00a0negative fourteen<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td><\/td>\r\n<td>[latex]n+n-4=-14[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td><\/td>\r\n<td>[latex]2n-4=-14[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add 4 to each side and simplify.<\/td>\r\n<td><\/td>\r\n<td>[latex]2n=-10[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide by 2.<\/td>\r\n<td><\/td>\r\n<td>[latex]n=-5[\/latex] \u00a0 \u00a0 1st number<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]n=-5[\/latex] to find the 2<sup>nd<\/sup> number.<\/td>\r\n<td><\/td>\r\n<td>[latex]n-4[\/latex] \u00a0 \u00a0 2nd number<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>[latex]\\color{red}{-5}-4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>[latex]-9[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is \u22129 four less than \u22125?Is their sum \u221214?<\/td>\r\n<td>[latex]-5-4\\stackrel{\\text{?}}{=}-9[\/latex][latex]-9=-9\\quad\\checkmark[\/latex]\r\n\r\n[latex]-5+(-9)\\stackrel{\\text{?}}{=}-14[\/latex]\r\n\r\n[latex]-14=-14\\quad\\checkmark[\/latex]<\/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><\/td>\r\n<td>The numbers are [latex]\u22125[\/latex] and [latex]\u22129[\/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&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n&nbsp;\r\n\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142806&amp;theme=oea&amp;iframe_resize_id=mom80[\/embed]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nOne number is ten more than twice another. Their sum is one. Find the numbers.\r\n<p class=\"p1\">[reveal-answer q=\"456765\"]Show Solution[\/reveal-answer]<\/p>\r\n<p class=\"p1\">[hidden-answer a=\"456765\"]<\/p>\r\nSolution:\r\n<table id=\"eip-id1168468367283\" class=\"unnumbered unstyled\" summary=\"Step 1 says 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<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><\/td>\r\n<td>two numbers<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong> Choose a variable.One number is ten more than twice another.<\/td>\r\n<td><\/td>\r\n<td>Let [latex]x=\\text{1st number}[\/latex][latex]2x+10={2}^{\\text{nd}}\\text{number}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong> Restate as one sentence.<\/td>\r\n<td><\/td>\r\n<td>Their sum is one.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Translate into an equation<\/td>\r\n<td><\/td>\r\n<td>[latex]x+(2x+10)\\enspace\\Rightarrow[\/latex] The sum of the two numbers[latex]=\\enspace\\Rightarrow[\/latex] is\r\n\r\n[latex]1\\enspace\\Rightarrow[\/latex] one<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td><\/td>\r\n<td>[latex]x+2x+10=1[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td><\/td>\r\n<td>[latex]3x+10=1[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract 10 from each side.<\/td>\r\n<td><\/td>\r\n<td>[latex]3x=-9[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide each side by 3 to get the first number.<\/td>\r\n<td><\/td>\r\n<td>[latex]x=-3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute to get the second number.<\/td>\r\n<td><\/td>\r\n<td>[latex]2x+10[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>[latex]2(\\color{red}{-3})+10[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>[latex]4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check.<\/strong><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Is 4 ten more than twice \u22123?Is their sum 1?<\/td>\r\n<td>[latex]2(-3)+10\\stackrel{\\text{?}}{=}4[\/latex][latex]-6+10=4[\/latex]\r\n\r\n[latex]4=4\\quad\\checkmark[\/latex]\r\n\r\n[latex]-3+4\\stackrel{\\text{?}}{=}1[\/latex]\r\n\r\n[latex]1=1\\quad\\checkmark[\/latex]<\/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><\/td>\r\n<td>The numbers are [latex]\u22123[\/latex] and [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&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142811&amp;theme=oea&amp;iframe_resize_id=mom90[\/embed]\r\n\r\n<\/div>\r\n<h2>Solving for Consecutive Integers<\/h2>\r\nAnother type of number problem involves consecutive numbers. Consecutive numbers are numbers that come one after the other.\u00a0\u00a0Some examples of consecutive integers are:\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c} \\hfill \\text{...}1, 2, 3, 4, 5, 6\\text{,...}\\hfill \\end{array}[\/latex]\r\n[latex]\\text{...}-10,-9,-8,-7\\text{,...}[\/latex]\r\n[latex]\\text{...}150,151,152,153\\text{,...}[\/latex]<\/p>\r\nIf we are looking for several consecutive numbers, it is important to first identify what they look like with variables before we set up the equation.\u00a0 Notice that each number is one more than the number preceding it. So if we define the first integer as [latex]n[\/latex], the next consecutive integer is [latex]n+1[\/latex]. The one after that is one more than [latex]n+1[\/latex], so it is [latex]n+1+1[\/latex], or [latex]n+2[\/latex].\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{cccc}n\\hfill &amp; &amp; &amp; \\text{1st integer}\\hfill \\\\ n+1\\hfill &amp; &amp; &amp; \\text{2nd consecutive integer}\\hfill \\\\ n+2\\hfill &amp; &amp; &amp; \\text{3rd consecutive integer}\\hfill \\end{array}[\/latex]<\/p>\r\nFor example, let's say I want to know the next consecutive integer after [latex]4[\/latex]. In mathematical terms, we would add [latex]1[\/latex] to [latex]4[\/latex] to get [latex]5[\/latex]. We can generalize this idea as follows: the consecutive integer of any number, [latex]x[\/latex], is [latex]x+1[\/latex]. If we continue this pattern, we can define any number of consecutive integers from any starting point. The following table shows how to describe four consecutive integers using algebraic notation.\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>First<\/td>\r\n<td>[latex]x[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Second<\/td>\r\n<td>[latex]x+1[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Third<\/td>\r\n<td>[latex]x+2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Fourth<\/td>\r\n<td>\u00a0[latex]x+3[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWe apply the idea of consecutive integers to solving a word problem in the following example.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe sum of two consecutive integers is [latex]47[\/latex]. Find the numbers.\r\n\r\nSolution:\r\n<table id=\"eip-id1168466146744\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem.<\/td>\r\n<td><\/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><\/td>\r\n<td>two consecutive integers<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong><\/td>\r\n<td><\/td>\r\n<td>Let [latex]n=\\text{1st integer}[\/latex]\r\n[latex]n+1=\\text{next consecutive integer}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong> Restate as one sentence.\r\nTranslate into an equation.<\/td>\r\n<td><\/td>\r\n<td>[latex]n+n+1\\enspace\\Rightarrow[\/latex] The sum of the integers\r\n[latex]=\\enspace\\Rightarrow[\/latex] is\r\n[latex]47\\enspace\\Rightarrow[\/latex]\u00a047<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td><\/td>\r\n<td>[latex]n+n+1=47[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td><\/td>\r\n<td>[latex]2n+1=47[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract 1 from each side.<\/td>\r\n<td><\/td>\r\n<td>[latex]2n=46[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide each side by 2.<\/td>\r\n<td><\/td>\r\n<td>[latex]n=23[\/latex] \u00a0 \u00a0 \u00a01st integer<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute to get the second number.<\/td>\r\n<td><\/td>\r\n<td>[latex]n+1[\/latex] \u00a0 \u00a0 2nd integer<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>[latex]\\color{red}{23}+1[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>[latex]24[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong><\/td>\r\n<td>[latex]23+24\\stackrel{\\text{?}}{=}47[\/latex]\r\n[latex]47=47\\quad\\checkmark[\/latex]<\/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><\/td>\r\n<td>The two consecutive integers are [latex]23[\/latex] and [latex]24[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]142817[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nThe sum of three consecutive integers is\u00a0[latex]93[\/latex]. What are the integers?\r\n\r\n[reveal-answer q=\"120402\"]Show Solution[\/reveal-answer]\r\n\r\n[hidden-answer a=\"120402\"]\r\nFollowing the steps provided:\r\n<ol>\r\n \t<li><strong>Read and understand:<\/strong>\u00a0We are looking for three numbers, and we know they are consecutive integers.<\/li>\r\n \t<li><strong>Constants and Variables: <\/strong>[latex]93[\/latex] is a constant.\r\nThe first integer we will call [latex]x[\/latex].\r\nSecond integer: [latex]x+1[\/latex]\r\nThird integer: [latex]x+2[\/latex]<\/li>\r\n \t<li><strong>Translate:\u00a0<\/strong>The sum of three consecutive integers translates to [latex]x+\\left(x+1\\right)+\\left(x+2\\right)[\/latex], based on how we defined the first, second, and third integers. Notice how we placed parentheses around the second and third integers. This is just to make each integer more distinct. \"<em>is 93<\/em>\" translates to \"[latex]=93[\/latex]\" since \"<em>is<\/em>\" is associated with equals.<\/li>\r\n \t<li><strong>Write an equation:<\/strong>\u00a0[latex]x+\\left(x+1\\right)+\\left(x+2\\right)=93[\/latex]<\/li>\r\n \t<li><strong>Solve the equation using what you know about solving linear equations:\u00a0<\/strong>We can't simplify within each set of parentheses, and we don't need to use the distributive property so we can rewrite the equation without parentheses.\r\n<p style=\"text-align: center;\">[latex]x+x+1+x+2=93[\/latex]<\/p>\r\nCombine like terms, simplify, and solve.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}x+x+1+x+2=93\\\\3x+3 = 93\\\\\\underline{-3\\,\\,\\,\\,\\,-3}\\\\3x=90\\\\\\frac{3x}{3}=\\frac{90}{3}\\\\x=30\\end{array}[\/latex]<\/p>\r\n<\/li>\r\n \t<li><strong>Check and Interpret:<\/strong> Okay, we have found a value for [latex]x[\/latex]. We were asked to find the value of three consecutive integers, so we need to do a couple more steps. Remember how we defined our variables:<\/li>\r\n<\/ol>\r\n<p style=\"padding-left: 90px;\">The first integer we will call [latex]x[\/latex], [latex]x=30[\/latex]\r\nSecond integer: [latex]x+1[\/latex] so [latex]30+1=31[\/latex]\r\nThird integer: [latex]x+2[\/latex] so [latex]30+2=32[\/latex]\r\nThe three consecutive integers whose sum is [latex]93[\/latex] are [latex]30\\text{, }31\\text{, and }32[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nFind three consecutive integers whose sum is [latex]42[\/latex].\r\n<p class=\"p1\">[reveal-answer q=\"367844\"]Show Solution[\/reveal-answer]<\/p>\r\n<p class=\"p1\">[hidden-answer a=\"367844\"]<\/p>\r\nSolution:\r\n<table id=\"eip-id1168466297040\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. <strong>Read<\/strong> the problem.<\/td>\r\n<td><\/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><\/td>\r\n<td>three consecutive integers<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. <strong>Name.<\/strong><\/td>\r\n<td><\/td>\r\n<td>Let [latex]n=\\text{1st integer}[\/latex][latex]n+1=\\text{2nd consecutive integer}[\/latex]\r\n\r\n[latex]n+2=\\text{3rd consecutive integer}[\/latex]\r\n\r\n&nbsp;<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. <strong>Translate.<\/strong> Restate as one sentence.\r\nTranslate into an equation.<\/td>\r\n<td><\/td>\r\n<td>[latex]n\\enspace +\\enspace n+1\\enspace +\\enspace n+2\\enspace\\Rightarrow[\/latex]\u00a0The sum of the three integers\r\n[latex]=\\enspace\\Rightarrow[\/latex] is\r\n[latex]42\\enspace\\Rightarrow[\/latex] 42<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\r\n<td><\/td>\r\n<td>[latex]n+n+1+n+2=42[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td><\/td>\r\n<td>[latex]3n+3=42[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract 3 from each side.<\/td>\r\n<td><\/td>\r\n<td>[latex]3n=39[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide each side by 3.<\/td>\r\n<td><\/td>\r\n<td>[latex]n=13[\/latex] \u00a0 \u00a0 \u00a01st integer<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute to get the second number.<\/td>\r\n<td><\/td>\r\n<td>[latex]n+1[\/latex] \u00a0 \u00a0 2nd integer<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>[latex]\\color{red}{13}+1[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>[latex]24[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute to get the third number.<\/td>\r\n<td><\/td>\r\n<td>[latex]n+2[\/latex] \u00a0 \u00a0 3rd integer<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>[latex]\\color{red}{13}+2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>[latex]15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 6. <strong>Check:<\/strong><\/td>\r\n<td>[latex]13+14+15\\stackrel{\\text{?}}{=}42[\/latex][latex]42=42\\quad\\checkmark[\/latex]<\/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><\/td>\r\n<td>The three consecutive integers are [latex]13[\/latex], [latex]14[\/latex], and [latex]15[\/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[ohm_question]142816[\/ohm_question]\r\n\r\n<\/div>\r\nWatch this video for another example of how to find three consecutive integers given their sum.\r\n\r\nhttps:\/\/youtu.be\/Bo67B0L9hGs\r\n\r\nIn the following video we show an example of a consecutive integer problem in which you are given the sum of four consecutive integers.\r\nhttps:\/\/youtu.be\/S5HZy3jKodg\r\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Solve number problems<\/li>\n<li>Solve consecutive integer problems<\/li>\n<\/ul>\n<\/div>\n<h2>Solving Number Problems<\/h2>\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 thirteen. 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. Translate into an equation.<\/td>\n<td>\u00a0[latex]n-6\\enspace\\Rightarrow[\/latex] The difference of a number and 6<br \/>\n[latex]=\\enspace\\Rightarrow[\/latex] is<br \/>\n[latex]13\\enspace\\Rightarrow[\/latex] thirteen<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation. Add 6 to both sides.<br \/>\nSimplify.<\/td>\n<td>[latex]n-6=13[\/latex]<br \/>\n[latex]n-6\\color{red}{+6}=13\\color{red}{+6}[\/latex]<br \/>\n[latex]n=19[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong>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<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p>&nbsp;<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm142763\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142763&#38;theme=oea&#38;iframe_resize_id=ohm142763&#38;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>The sum of twice a number and seven is fifteen. 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 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-id1168468309891\" class=\"unnumbered unstyled\" summary=\"Step 1 says 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>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 the problem as one sentence.<br \/>\nTranslate into an equation.<\/td>\n<td>[latex]2n\\enspace\\Rightarrow[\/latex] The sum of twice a number<br \/>\n[latex]+\\enspace\\Rightarrow[\/latex] and<br \/>\n[latex]7\\enspace\\Rightarrow[\/latex] seven<br \/>\n[latex]=\\enspace\\Rightarrow[\/latex] is<br \/>\n[latex]15\\enspace\\Rightarrow[\/latex] fifteen<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td>[latex]2n+7=15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract 7 from each side and simplify.<\/td>\n<td>[latex]2n=8[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide each side by 2 and simplify.<\/td>\n<td>[latex]n=4[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong> is the sum of twice [latex]4[\/latex] and [latex]7[\/latex] equal to [latex]15[\/latex]?<\/td>\n<td>[latex]2\\cdot{4}+7=15[\/latex]<br \/>\n[latex]8+7=15[\/latex]<br \/>\n[latex]15=15\\quad\\checkmark[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td>The number is [latex]4[\/latex].<\/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 it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm142770\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142770&#38;theme=oea&#38;iframe_resize_id=ohm142770&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/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<h3>Solving for Two or More Numbers<\/h3>\n<p>Some number word problems ask you to find two or more numbers. It may be tempting to name them all with different variables, but so far we have only solved equations with one variable. We will define the numbers in terms of the same variable. Be sure to read the problem carefully to discover how all the numbers relate to each other.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>One number is five more than another. The sum of the numbers is twenty-one. Find the numbers.<\/p>\n<p class=\"p1\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q200999\">Show Solution<\/span><\/p>\n<p class=\"p1\">\n<div id=\"q200999\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466015145\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem.<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td><\/td>\n<td>You are looking for two numbers.<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong>Choose a variable to represent the first number.<\/p>\n<p>What do you know about the second number?<\/p>\n<p>Translate.<\/td>\n<td><\/td>\n<td>Let [latex]n=\\text{1st number}[\/latex]One number is five more than another.<\/p>\n<p>[latex]n+5={2}^{\\text{nd}}\\text{number}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong>Restate the problem as one sentence with all the important information.<\/p>\n<p>Translate into an equation.<\/p>\n<p>Substitute the variable expressions.<\/td>\n<td><\/td>\n<td>The sum of the numbers is [latex]21[\/latex].The sum of the 1st number and the 2nd number is [latex]21[\/latex].<\/p>\n<p>[latex]n\\enspace\\Rightarrow[\/latex]\u00a0First number<\/p>\n<p>[latex]+\\enspace\\Rightarrow[\/latex] +<\/p>\n<p>[latex]n+5\\enspace\\Rightarrow[\/latex] Second number<\/p>\n<p>[latex]=\\enspace\\Rightarrow[\/latex]\u00a0=<\/p>\n<p>[latex]21\\enspace\\Rightarrow[\/latex]\u00a0twenty-one<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td><\/td>\n<td>[latex]n+n+5=21[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><\/td>\n<td>[latex]2n+5=21[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract five from both sides and simplify.<\/td>\n<td><\/td>\n<td>[latex]2n=16[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide by two and simplify.<\/td>\n<td><\/td>\n<td>[latex]n=8[\/latex] \u00a0 \u00a0 1st number<\/td>\n<\/tr>\n<tr>\n<td>Now find the second number.<\/td>\n<td><\/td>\n<td>[latex]n+5[\/latex] \u00a0 \u00a0 2nd number<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]n = 8[\/latex]<\/td>\n<td><\/td>\n<td>[latex]\\color{red}{8}+5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>[latex]13[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Do these numbers check in the problem?Is one number 5 more than the other?<\/p>\n<p>Is thirteen, 5 more than 8? Yes.<\/p>\n<p>Is the sum of the two numbers 21?<\/td>\n<td>[latex]13\\stackrel{\\text{?}}{=}8+5[\/latex][latex]13=13\\quad\\checkmark[\/latex]<\/p>\n<p>[latex]8+13\\stackrel{\\text{?}}{=}21[\/latex]<\/p>\n<p>[latex]21=21\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td><\/td>\n<td>The numbers are [latex]8[\/latex] and [latex]13[\/latex].<\/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 it<\/h3>\n<p>&nbsp;<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm142775\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142775&#38;theme=oea&#38;iframe_resize_id=ohm142775&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video to see another example of how to find two numbers given the relationship between the two.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex:  Linear Equation Application with One Variable - Number Problem\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/juslHscrh8s?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3><\/h3>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The sum of two numbers is negative fourteen. One number is four less than the other. Find the numbers.<\/p>\n<p class=\"p1\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q500777\">Show Solution<\/span><\/p>\n<p class=\"p1\">\n<div id=\"q500777\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168469638662\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem.<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td><\/td>\n<td>two numbers<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable.What do you know about the second number?<\/p>\n<p>Translate.<\/td>\n<td><\/td>\n<td>Let [latex]n=\\text{1st number}[\/latex]One number is [latex]4[\/latex] less than the other.<\/p>\n<p>[latex]n-4={2}^{\\text{nd}}\\text{number}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong>Write as one sentence.<\/p>\n<p>Translate into an equation.<\/p>\n<p>Substitute the variable expressions.<\/td>\n<td><\/td>\n<td>The sum of two numbers is negative fourteen.[latex]n\\enspace\\Rightarrow[\/latex]\u00a0First number<\/p>\n<p>[latex]+\\enspace\\Rightarrow[\/latex]\u00a0+<\/p>\n<p>[latex]n-4\\enspace\\Rightarrow[\/latex] Second number<\/p>\n<p>[latex]=\\enspace\\Rightarrow[\/latex]\u00a0=<\/p>\n<p>[latex]-14\\enspace\\Rightarrow[\/latex]\u00a0negative fourteen<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td><\/td>\n<td>[latex]n+n-4=-14[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><\/td>\n<td>[latex]2n-4=-14[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add 4 to each side and simplify.<\/td>\n<td><\/td>\n<td>[latex]2n=-10[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide by 2.<\/td>\n<td><\/td>\n<td>[latex]n=-5[\/latex] \u00a0 \u00a0 1st number<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]n=-5[\/latex] to find the 2<sup>nd<\/sup> number.<\/td>\n<td><\/td>\n<td>[latex]n-4[\/latex] \u00a0 \u00a0 2nd number<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>[latex]\\color{red}{-5}-4[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>[latex]-9[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is \u22129 four less than \u22125?Is their sum \u221214?<\/td>\n<td>[latex]-5-4\\stackrel{\\text{?}}{=}-9[\/latex][latex]-9=-9\\quad\\checkmark[\/latex]<\/p>\n<p>[latex]-5+(-9)\\stackrel{\\text{?}}{=}-14[\/latex]<\/p>\n<p>[latex]-14=-14\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td><\/td>\n<td>The numbers are [latex]\u22125[\/latex] and [latex]\u22129[\/latex].<\/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 it<\/h3>\n<p>&nbsp;<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm142806\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142806&#38;theme=oea&#38;iframe_resize_id=ohm142806&#38;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 number is ten more than twice another. Their sum is one. Find the numbers.<\/p>\n<p class=\"p1\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q456765\">Show Solution<\/span><\/p>\n<p class=\"p1\">\n<div id=\"q456765\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468367283\" class=\"unnumbered unstyled\" summary=\"Step 1 says to read the problem.\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem.<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td><\/td>\n<td>two numbers<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong> Choose a variable.One number is ten more than twice another.<\/td>\n<td><\/td>\n<td>Let [latex]x=\\text{1st number}[\/latex][latex]2x+10={2}^{\\text{nd}}\\text{number}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong> Restate as one sentence.<\/td>\n<td><\/td>\n<td>Their sum is one.<\/td>\n<\/tr>\n<tr>\n<td>Translate into an equation<\/td>\n<td><\/td>\n<td>[latex]x+(2x+10)\\enspace\\Rightarrow[\/latex] The sum of the two numbers[latex]=\\enspace\\Rightarrow[\/latex] is<\/p>\n<p>[latex]1\\enspace\\Rightarrow[\/latex] one<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td><\/td>\n<td>[latex]x+2x+10=1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><\/td>\n<td>[latex]3x+10=1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract 10 from each side.<\/td>\n<td><\/td>\n<td>[latex]3x=-9[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide each side by 3 to get the first number.<\/td>\n<td><\/td>\n<td>[latex]x=-3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute to get the second number.<\/td>\n<td><\/td>\n<td>[latex]2x+10[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>[latex]2(\\color{red}{-3})+10[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>[latex]4[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check.<\/strong><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Is 4 ten more than twice \u22123?Is their sum 1?<\/td>\n<td>[latex]2(-3)+10\\stackrel{\\text{?}}{=}4[\/latex][latex]-6+10=4[\/latex]<\/p>\n<p>[latex]4=4\\quad\\checkmark[\/latex]<\/p>\n<p>[latex]-3+4\\stackrel{\\text{?}}{=}1[\/latex]<\/p>\n<p>[latex]1=1\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td><\/td>\n<td>The numbers are [latex]\u22123[\/latex] and [latex]4[\/latex].<\/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 it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm142811\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142811&#38;theme=oea&#38;iframe_resize_id=ohm142811&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h2>Solving for Consecutive Integers<\/h2>\n<p>Another type of number problem involves consecutive numbers. Consecutive numbers are numbers that come one after the other.\u00a0\u00a0Some examples of consecutive integers are:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c} \\hfill \\text{...}1, 2, 3, 4, 5, 6\\text{,...}\\hfill \\end{array}[\/latex]<br \/>\n[latex]\\text{...}-10,-9,-8,-7\\text{,...}[\/latex]<br \/>\n[latex]\\text{...}150,151,152,153\\text{,...}[\/latex]<\/p>\n<p>If we are looking for several consecutive numbers, it is important to first identify what they look like with variables before we set up the equation.\u00a0 Notice that each number is one more than the number preceding it. So if we define the first integer as [latex]n[\/latex], the next consecutive integer is [latex]n+1[\/latex]. The one after that is one more than [latex]n+1[\/latex], so it is [latex]n+1+1[\/latex], or [latex]n+2[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{cccc}n\\hfill & & & \\text{1st integer}\\hfill \\\\ n+1\\hfill & & & \\text{2nd consecutive integer}\\hfill \\\\ n+2\\hfill & & & \\text{3rd consecutive integer}\\hfill \\end{array}[\/latex]<\/p>\n<p>For example, let&#8217;s say I want to know the next consecutive integer after [latex]4[\/latex]. In mathematical terms, we would add [latex]1[\/latex] to [latex]4[\/latex] to get [latex]5[\/latex]. We can generalize this idea as follows: the consecutive integer of any number, [latex]x[\/latex], is [latex]x+1[\/latex]. If we continue this pattern, we can define any number of consecutive integers from any starting point. The following table shows how to describe four consecutive integers using algebraic notation.<\/p>\n<table>\n<tbody>\n<tr>\n<td>First<\/td>\n<td>[latex]x[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Second<\/td>\n<td>[latex]x+1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Third<\/td>\n<td>[latex]x+2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Fourth<\/td>\n<td>\u00a0[latex]x+3[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>We apply the idea of consecutive integers to solving a word problem in the following example.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The sum of two consecutive integers is [latex]47[\/latex]. Find the numbers.<\/p>\n<p>Solution:<\/p>\n<table id=\"eip-id1168466146744\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem.<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td><\/td>\n<td>two consecutive integers<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong><\/td>\n<td><\/td>\n<td>Let [latex]n=\\text{1st integer}[\/latex]<br \/>\n[latex]n+1=\\text{next consecutive integer}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong> Restate as one sentence.<br \/>\nTranslate into an equation.<\/td>\n<td><\/td>\n<td>[latex]n+n+1\\enspace\\Rightarrow[\/latex] The sum of the integers<br \/>\n[latex]=\\enspace\\Rightarrow[\/latex] is<br \/>\n[latex]47\\enspace\\Rightarrow[\/latex]\u00a047<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td><\/td>\n<td>[latex]n+n+1=47[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><\/td>\n<td>[latex]2n+1=47[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract 1 from each side.<\/td>\n<td><\/td>\n<td>[latex]2n=46[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide each side by 2.<\/td>\n<td><\/td>\n<td>[latex]n=23[\/latex] \u00a0 \u00a0 \u00a01st integer<\/td>\n<\/tr>\n<tr>\n<td>Substitute to get the second number.<\/td>\n<td><\/td>\n<td>[latex]n+1[\/latex] \u00a0 \u00a0 2nd integer<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>[latex]\\color{red}{23}+1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>[latex]24[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong><\/td>\n<td>[latex]23+24\\stackrel{\\text{?}}{=}47[\/latex]<br \/>\n[latex]47=47\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td><\/td>\n<td>The two consecutive integers are [latex]23[\/latex] and [latex]24[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm142817\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142817&theme=oea&iframe_resize_id=ohm142817&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>The sum of three consecutive integers is\u00a0[latex]93[\/latex]. What are the integers?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q120402\">Show Solution<\/span><\/p>\n<div id=\"q120402\" class=\"hidden-answer\" style=\"display: none\">\nFollowing the steps provided:<\/p>\n<ol>\n<li><strong>Read and understand:<\/strong>\u00a0We are looking for three numbers, and we know they are consecutive integers.<\/li>\n<li><strong>Constants and Variables: <\/strong>[latex]93[\/latex] is a constant.<br \/>\nThe first integer we will call [latex]x[\/latex].<br \/>\nSecond integer: [latex]x+1[\/latex]<br \/>\nThird integer: [latex]x+2[\/latex]<\/li>\n<li><strong>Translate:\u00a0<\/strong>The sum of three consecutive integers translates to [latex]x+\\left(x+1\\right)+\\left(x+2\\right)[\/latex], based on how we defined the first, second, and third integers. Notice how we placed parentheses around the second and third integers. This is just to make each integer more distinct. &#8220;<em>is 93<\/em>&#8221; translates to &#8220;[latex]=93[\/latex]&#8221; since &#8220;<em>is<\/em>&#8221; is associated with equals.<\/li>\n<li><strong>Write an equation:<\/strong>\u00a0[latex]x+\\left(x+1\\right)+\\left(x+2\\right)=93[\/latex]<\/li>\n<li><strong>Solve the equation using what you know about solving linear equations:\u00a0<\/strong>We can&#8217;t simplify within each set of parentheses, and we don&#8217;t need to use the distributive property so we can rewrite the equation without parentheses.\n<p style=\"text-align: center;\">[latex]x+x+1+x+2=93[\/latex]<\/p>\n<p>Combine like terms, simplify, and solve.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}x+x+1+x+2=93\\\\3x+3 = 93\\\\\\underline{-3\\,\\,\\,\\,\\,-3}\\\\3x=90\\\\\\frac{3x}{3}=\\frac{90}{3}\\\\x=30\\end{array}[\/latex]<\/p>\n<\/li>\n<li><strong>Check and Interpret:<\/strong> Okay, we have found a value for [latex]x[\/latex]. We were asked to find the value of three consecutive integers, so we need to do a couple more steps. Remember how we defined our variables:<\/li>\n<\/ol>\n<p style=\"padding-left: 90px;\">The first integer we will call [latex]x[\/latex], [latex]x=30[\/latex]<br \/>\nSecond integer: [latex]x+1[\/latex] so [latex]30+1=31[\/latex]<br \/>\nThird integer: [latex]x+2[\/latex] so [latex]30+2=32[\/latex]<br \/>\nThe three consecutive integers whose sum is [latex]93[\/latex] are [latex]30\\text{, }31\\text{, and }32[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Find three consecutive integers whose sum is [latex]42[\/latex].<\/p>\n<p class=\"p1\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q367844\">Show Solution<\/span><\/p>\n<p class=\"p1\">\n<div id=\"q367844\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466297040\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Step 1. <strong>Read<\/strong> the problem.<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong>Identify<\/strong> what you are looking for.<\/td>\n<td><\/td>\n<td>three consecutive integers<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong>Name.<\/strong><\/td>\n<td><\/td>\n<td>Let [latex]n=\\text{1st integer}[\/latex][latex]n+1=\\text{2nd consecutive integer}[\/latex]<\/p>\n<p>[latex]n+2=\\text{3rd consecutive integer}[\/latex]<\/p>\n<p>&nbsp;<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong>Translate.<\/strong> Restate as one sentence.<br \/>\nTranslate into an equation.<\/td>\n<td><\/td>\n<td>[latex]n\\enspace +\\enspace n+1\\enspace +\\enspace n+2\\enspace\\Rightarrow[\/latex]\u00a0The sum of the three integers<br \/>\n[latex]=\\enspace\\Rightarrow[\/latex] is<br \/>\n[latex]42\\enspace\\Rightarrow[\/latex] 42<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong>Solve<\/strong> the equation.<\/td>\n<td><\/td>\n<td>[latex]n+n+1+n+2=42[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><\/td>\n<td>[latex]3n+3=42[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract 3 from each side.<\/td>\n<td><\/td>\n<td>[latex]3n=39[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide each side by 3.<\/td>\n<td><\/td>\n<td>[latex]n=13[\/latex] \u00a0 \u00a0 \u00a01st integer<\/td>\n<\/tr>\n<tr>\n<td>Substitute to get the second number.<\/td>\n<td><\/td>\n<td>[latex]n+1[\/latex] \u00a0 \u00a0 2nd integer<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>[latex]\\color{red}{13}+1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>[latex]24[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute to get the third number.<\/td>\n<td><\/td>\n<td>[latex]n+2[\/latex] \u00a0 \u00a0 3rd integer<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>[latex]\\color{red}{13}+2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>[latex]15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong>Check:<\/strong><\/td>\n<td>[latex]13+14+15\\stackrel{\\text{?}}{=}42[\/latex][latex]42=42\\quad\\checkmark[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong>Answer<\/strong> the question.<\/td>\n<td><\/td>\n<td>The three consecutive integers are [latex]13[\/latex], [latex]14[\/latex], and [latex]15[\/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=\"ohm142816\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142816&theme=oea&iframe_resize_id=ohm142816&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch this video for another example of how to find three consecutive integers given their sum.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Ex: Write and Solve an Equation for Consecutive Natural Numbers with a Given Sum\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/Bo67B0L9hGs?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>In the following video we show an example of a consecutive integer problem in which you are given the sum of four consecutive integers.<br \/>\n<iframe loading=\"lazy\" id=\"oembed-4\" title=\"Write and Solve a Linear Equations to Solve a Number Problem (Consecutive Integers)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/S5HZy3jKodg?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-9121\">\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>Ex: Linear Equation Application with One Variable - Number Problem. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/juslHscrh8s\">https:\/\/youtu.be\/juslHscrh8s<\/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: Write and Solve an Equation for Consecutive Natural Numbers with a Given Sum. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/Bo67B0L9hGs\">https:\/\/youtu.be\/Bo67B0L9hGs<\/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>Write and Solve a Linear Equations to Solve a Number Problem (1) Mathispower4u . <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/izIIqOztUyI\">https:\/\/youtu.be\/izIIqOztUyI<\/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 142763, 142770, 142775, 142806, 142811, 142816, 142817. <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":15,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Ex: Linear Equation Application with One Variable - 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