{"id":2619,"date":"2016-11-04T18:05:12","date_gmt":"2016-11-04T18:05:12","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebra\/?post_type=chapter&#038;p=2619"},"modified":"2025-10-15T22:49:25","modified_gmt":"2025-10-15T22:49:25","slug":"write-a-linear-equation-to-solve-an-application","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebra\/chapter\/write-a-linear-equation-to-solve-an-application\/","title":{"raw":"Writing a Linear Equation to Solve an Application","rendered":"Writing a Linear Equation to Solve an Application"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Write a linear equation to express the relationship between unknown quantities.<\/li>\r\n \t<li>Write a linear equation that models two different cell phone packages.<\/li>\r\n \t<li>Use a linear model to answer questions.<\/li>\r\n<\/ul>\r\n<\/div>\r\nTo set up or model a linear equation to fit a real-world application, we must first determine the known quantities and define the unknown quantity as a variable. Then, we begin to interpret the words as mathematical expressions using mathematical symbols. Let us use the car rental example above. In this case, a known cost, such as $0.10\/mi, is multiplied by an unknown quantity, the number of miles driven. Therefore, we can write [latex]0.10x[\/latex]. This expression represents a variable cost because it changes according to the number of miles driven.\r\n\r\nIf a quantity is independent of a variable, we usually just add or subtract it according to the problem. As these amounts do not change, we call them fixed costs. Consider a car rental agency that charges $0.10\/mi plus a daily fee of $50. We can use these quantities to model an equation that can be used to find the daily car rental cost [latex]C[\/latex].\r\n<div style=\"text-align: center\">[latex]C=0.10x+50[\/latex]<\/div>\r\nWhen dealing with real-world applications, there are certain expressions that we can translate directly into math. The table\u00a0lists some common verbal expressions and their equivalent mathematical expressions.\r\n<table summary=\"A table with 8 rows and 2 columns. The entries in the first row are: Verbal and Translation to math operations. The entries in the second row are: One number exceeds another by a and x, x+a. The entries in the third row are: Twice a number and 2x. The entries in the fourth row are: One number is a more than another number and x, x plus a. The entries in the fifth row are: One number is a less than twice another number and x,2 times x minus a. The entries in the sixth row are: The product of a number and a, decreased by b and a times x minus b. The entries in the seventh row are: The quotient of a number and the number plus a is three times the number and x divided by the quantity x plus a equals three times x. The entries in the eighth row are: The product of three times a number and the number decreased by b is c and three times x times the quantity x minus b equals c.\">\r\n<thead>\r\n<tr>\r\n<th><strong>Verbal<\/strong><\/th>\r\n<th><strong>Translation to Math Operations<\/strong><\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td><strong>One number exceeds another by <em>a<\/em><\/strong><\/td>\r\n<td><strong>[latex]x,\\text{ }x+a[\/latex]<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Twice a number<\/strong><\/td>\r\n<td><strong>[latex]2x[\/latex]<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>One number is <em>a <\/em>more than another number<\/strong><\/td>\r\n<td><strong>[latex]x,\\text{ }x+a[\/latex]<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>One number is <em>a <\/em>less than twice another number<\/strong><\/td>\r\n<td><strong>[latex]x,2x-a[\/latex]<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>The product of a number and <em>a<\/em>, decreased by <em>b<\/em><\/strong><\/td>\r\n<td><strong>[latex]ax-b[\/latex]<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>The quotient of a number and the number plus <em>a <\/em>is three times the number<\/strong><\/td>\r\n<td><strong>[latex]\\frac{x}{x+a}=3x[\/latex]<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>The product of three times a number and the number decreased by <em>b <\/em>is <em>c<\/em><\/strong><\/td>\r\n<td><strong>[latex]3x\\left(x-b\\right)=c[\/latex]<\/strong><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox\">\r\n<h3>How To: Given a real-world problem, model a linear equation to fit it<\/h3>\r\n<ol>\r\n \t<li>Identify known quantities.<\/li>\r\n \t<li>Assign a variable to represent the unknown quantity.<\/li>\r\n \t<li>If there is more than one unknown quantity, find a way to write the second unknown in terms of the first.<\/li>\r\n \t<li>Write an equation interpreting the words as mathematical operations.<\/li>\r\n \t<li>Solve the equation. Be sure the solution can be explained in words including the units of measure.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example: Modeling a Linear Equation to Solve an Unknown Number Problem<\/h3>\r\nFind a linear equation to solve for the following unknown quantities: One number exceeds another number by [latex]17[\/latex] and their sum is [latex]31[\/latex]. Find the two numbers.\r\n[reveal-answer q=\"760873\"]Show Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"760873\"]\r\n\r\nLet [latex]x[\/latex] equal the first number. Then, as the second number exceeds the first by 17, we can write the second number as [latex]x+17[\/latex]. The sum of the two numbers is 31. We usually interpret the word <em>is<\/em> as an equal sign.\r\n<div style=\"text-align: center\">[latex]\\begin{array}{ll}x+\\left(x+17\\right)=31\\hfill \\\\ 2x+17=31\\hfill&amp;\\text{Simplify and solve}.\\hfill &amp; \\\\ 2x=14\\hfill \\\\ x=7\\hfill &amp; \\\\ \\hfill &amp; \\\\ x+17=7+17=24\\hfill \\end{array}[\/latex]<\/div>\r\nThe two numbers are [latex]7[\/latex] and [latex]24[\/latex].\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nFind a linear equation to solve for the following unknown quantities: One number is three more than twice another number. If the sum of the two numbers is [latex]36[\/latex], find the numbers.\r\n[reveal-answer q=\"930268\"]Show Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"930268\"]\r\n\r\n11 and 25[\/hidden-answer]<iframe id=\"mom1\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=7647&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"250\"><\/iframe>\r\n<iframe id=\"mom5\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=30987&amp;theme=oea&amp;iframe_resize_id=mom5\" width=\"100%\" height=\"250\"><\/iframe>\r\n<iframe id=\"mom6\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=13665&amp;theme=oea&amp;iframe_resize_id=mom6\" width=\"100%\" height=\"250\"><\/iframe>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example: Setting Up a Linear Equation to Solve a Real-World Application<\/h3>\r\nThere are two cell phone companies that offer different packages. Company A charges a monthly service fee of $34 plus $.05\/min talk-time. Company B charges a monthly service fee of $40 plus $.04\/min talk-time.\r\n<ol>\r\n \t<li>Write a linear equation that models the packages offered by both companies.<\/li>\r\n \t<li>If the average number of minutes used each month is 1,160, which company offers the better plan?<\/li>\r\n \t<li>If the average number of minutes used each month is 420, which company offers the better plan?<\/li>\r\n \t<li>How many minutes of talk-time would yield equal monthly statements from both companies?<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"785384\"]Show Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"785384\"]\r\n<ol>\r\n \t<li>The model for Company <em>A<\/em> can be written as [latex]A=0.05x+34[\/latex]. This includes the variable cost of [latex]0.05x[\/latex] plus the monthly service charge of $34. Company <em>B<\/em>\u2019s package charges a higher monthly fee of $40, but a lower variable cost of [latex]0.04x[\/latex]. Company <em>B<\/em>\u2019s model can be written as [latex]B=0.04x+40[\/latex].<\/li>\r\n \t<li>If the average number of minutes used each month is 1,160, we have the following:\r\n<div>[latex]\\begin{array}{l}\\text{Company }A\\hfill&amp;=0.05\\left(1,160\\right)+34\\hfill \\\\ \\hfill&amp;=58+34\\hfill \\\\ \\hfill&amp;=92\\hfill \\\\ \\hfill \\\\ \\text{Company }B\\hfill&amp;=0.04\\left(1,160\\right)+40\\hfill \\\\ \\hfill&amp;=46.4+40\\hfill \\\\ \\hfill&amp;=86.4\\hfill \\end{array}[\/latex]<\/div>\r\nSo, Company <em>B<\/em> offers the lower monthly cost of $86.40 as compared with the $92 monthly cost offered by Company <em>A<\/em> when the average number of minutes used each month is 1,160.<\/li>\r\n \t<li>If the average number of minutes used each month is 420, we have the following:\r\n<div>[latex]\\begin{array}{l}\\text{Company }A\\hfill&amp;=0.05\\left(420\\right)+34\\hfill \\\\ \\hfill&amp;=21+34\\hfill \\\\ \\hfill&amp;=55\\hfill \\\\ \\hfill \\\\ \\text{Company }B\\hfill&amp;=0.04\\left(420\\right)+40\\hfill \\\\ \\hfill&amp;=16.8+40\\hfill \\\\ \\hfill&amp;=56.8\\hfill \\end{array}[\/latex]<\/div>\r\nIf the average number of minutes used each month is 420, then Company <em>A <\/em>offers a lower monthly cost of $55 compared to Company <em>B<\/em>\u2019s monthly cost of $56.80.<\/li>\r\n \t<li>To answer the question of how many talk-time minutes would yield the same bill from both companies, we should think about the problem in terms of [latex]\\left(x,y\\right)[\/latex] coordinates: At what point are both the <em>x-<\/em>value and the <em>y-<\/em>value equal? We can find this point by setting the equations equal to each other and solving for <em>x.<\/em>\r\n<div style=\"text-align: center\">[latex]\\begin{array}{l}0.05x+34=0.04x+40\\hfill \\\\ 0.01x=6\\hfill \\\\ x=600\\hfill \\end{array}[\/latex]<\/div>\r\nCheck the <em>x-<\/em>value in each equation.\r\n<div style=\"text-align: left\">[latex]\\begin{array}{l}0.05\\left(600\\right)+34=64\\hfill \\\\ 0.04\\left(600\\right)+40=64\\hfill \\end{array}[\/latex]<\/div>\r\nTherefore, a monthly average of 600 talk-time minutes renders the plans equal.<\/li>\r\n<\/ol>\r\n<ol>\r\n \t<li><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/09\/25200339\/CNX_CAT_Figure_02_03_002.jpg\" alt=\"Coordinate plane with the x-axis ranging from 0 to 1200 in intervals of 100 and the y-axis ranging from 0 to 90 in intervals of 10. The functions A = 0.05x + 34 and B = 0.04x + 40 are graphed on the same plot\" width=\"731\" height=\"420\" \/>\r\n\r\n[\/hidden-answer]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nFind a linear equation to model this real-world application: It costs ABC electronics company $2.50 per unit to produce a part used in a popular brand of desktop computers. The company has monthly operating expenses of $350 for utilities and $3,300 for salaries. What are the company\u2019s monthly expenses?\r\n[reveal-answer q=\"68149\"]Show Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"68149\"][latex]\r\n\r\nC=2.5x+3,650[\/latex][\/hidden-answer]<iframe id=\"mom1\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=92426&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"500\"><\/iframe>\r\n\r\n<\/div>\r\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Write a linear equation to express the relationship between unknown quantities.<\/li>\n<li>Write a linear equation that models two different cell phone packages.<\/li>\n<li>Use a linear model to answer questions.<\/li>\n<\/ul>\n<\/div>\n<p>To set up or model a linear equation to fit a real-world application, we must first determine the known quantities and define the unknown quantity as a variable. Then, we begin to interpret the words as mathematical expressions using mathematical symbols. Let us use the car rental example above. In this case, a known cost, such as $0.10\/mi, is multiplied by an unknown quantity, the number of miles driven. Therefore, we can write [latex]0.10x[\/latex]. This expression represents a variable cost because it changes according to the number of miles driven.<\/p>\n<p>If a quantity is independent of a variable, we usually just add or subtract it according to the problem. As these amounts do not change, we call them fixed costs. Consider a car rental agency that charges $0.10\/mi plus a daily fee of $50. We can use these quantities to model an equation that can be used to find the daily car rental cost [latex]C[\/latex].<\/p>\n<div style=\"text-align: center\">[latex]C=0.10x+50[\/latex]<\/div>\n<p>When dealing with real-world applications, there are certain expressions that we can translate directly into math. The table\u00a0lists some common verbal expressions and their equivalent mathematical expressions.<\/p>\n<table summary=\"A table with 8 rows and 2 columns. The entries in the first row are: Verbal and Translation to math operations. The entries in the second row are: One number exceeds another by a and x, x+a. The entries in the third row are: Twice a number and 2x. The entries in the fourth row are: One number is a more than another number and x, x plus a. The entries in the fifth row are: One number is a less than twice another number and x,2 times x minus a. The entries in the sixth row are: The product of a number and a, decreased by b and a times x minus b. The entries in the seventh row are: The quotient of a number and the number plus a is three times the number and x divided by the quantity x plus a equals three times x. The entries in the eighth row are: The product of three times a number and the number decreased by b is c and three times x times the quantity x minus b equals c.\">\n<thead>\n<tr>\n<th><strong>Verbal<\/strong><\/th>\n<th><strong>Translation to Math Operations<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>One number exceeds another by <em>a<\/em><\/strong><\/td>\n<td><strong>[latex]x,\\text{ }x+a[\/latex]<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>Twice a number<\/strong><\/td>\n<td><strong>[latex]2x[\/latex]<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>One number is <em>a <\/em>more than another number<\/strong><\/td>\n<td><strong>[latex]x,\\text{ }x+a[\/latex]<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>One number is <em>a <\/em>less than twice another number<\/strong><\/td>\n<td><strong>[latex]x,2x-a[\/latex]<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>The product of a number and <em>a<\/em>, decreased by <em>b<\/em><\/strong><\/td>\n<td><strong>[latex]ax-b[\/latex]<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>The quotient of a number and the number plus <em>a <\/em>is three times the number<\/strong><\/td>\n<td><strong>[latex]\\frac{x}{x+a}=3x[\/latex]<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>The product of three times a number and the number decreased by <em>b <\/em>is <em>c<\/em><\/strong><\/td>\n<td><strong>[latex]3x\\left(x-b\\right)=c[\/latex]<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox\">\n<h3>How To: Given a real-world problem, model a linear equation to fit it<\/h3>\n<ol>\n<li>Identify known quantities.<\/li>\n<li>Assign a variable to represent the unknown quantity.<\/li>\n<li>If there is more than one unknown quantity, find a way to write the second unknown in terms of the first.<\/li>\n<li>Write an equation interpreting the words as mathematical operations.<\/li>\n<li>Solve the equation. Be sure the solution can be explained in words including the units of measure.<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example: Modeling a Linear Equation to Solve an Unknown Number Problem<\/h3>\n<p>Find a linear equation to solve for the following unknown quantities: One number exceeds another number by [latex]17[\/latex] and their sum is [latex]31[\/latex]. Find the two numbers.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q760873\">Show Show Solution<\/span><\/p>\n<div id=\"q760873\" class=\"hidden-answer\" style=\"display: none\">\n<p>Let [latex]x[\/latex] equal the first number. Then, as the second number exceeds the first by 17, we can write the second number as [latex]x+17[\/latex]. The sum of the two numbers is 31. We usually interpret the word <em>is<\/em> as an equal sign.<\/p>\n<div style=\"text-align: center\">[latex]\\begin{array}{ll}x+\\left(x+17\\right)=31\\hfill \\\\ 2x+17=31\\hfill&\\text{Simplify and solve}.\\hfill & \\\\ 2x=14\\hfill \\\\ x=7\\hfill & \\\\ \\hfill & \\\\ x+17=7+17=24\\hfill \\end{array}[\/latex]<\/div>\n<p>The two numbers are [latex]7[\/latex] and [latex]24[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Find a linear equation to solve for the following unknown quantities: One number is three more than twice another number. If the sum of the two numbers is [latex]36[\/latex], find the numbers.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q930268\">Show Show Solution<\/span><\/p>\n<div id=\"q930268\" class=\"hidden-answer\" style=\"display: none\">\n<p>11 and 25<\/p><\/div>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"mom1\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=7647&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"250\"><\/iframe><br \/>\n<iframe loading=\"lazy\" id=\"mom5\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=30987&amp;theme=oea&amp;iframe_resize_id=mom5\" width=\"100%\" height=\"250\"><\/iframe><br \/>\n<iframe loading=\"lazy\" id=\"mom6\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=13665&amp;theme=oea&amp;iframe_resize_id=mom6\" width=\"100%\" height=\"250\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example: Setting Up a Linear Equation to Solve a Real-World Application<\/h3>\n<p>There are two cell phone companies that offer different packages. Company A charges a monthly service fee of $34 plus $.05\/min talk-time. Company B charges a monthly service fee of $40 plus $.04\/min talk-time.<\/p>\n<ol>\n<li>Write a linear equation that models the packages offered by both companies.<\/li>\n<li>If the average number of minutes used each month is 1,160, which company offers the better plan?<\/li>\n<li>If the average number of minutes used each month is 420, which company offers the better plan?<\/li>\n<li>How many minutes of talk-time would yield equal monthly statements from both companies?<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q785384\">Show Show Solution<\/span><\/p>\n<div id=\"q785384\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>The model for Company <em>A<\/em> can be written as [latex]A=0.05x+34[\/latex]. This includes the variable cost of [latex]0.05x[\/latex] plus the monthly service charge of $34. Company <em>B<\/em>\u2019s package charges a higher monthly fee of $40, but a lower variable cost of [latex]0.04x[\/latex]. Company <em>B<\/em>\u2019s model can be written as [latex]B=0.04x+40[\/latex].<\/li>\n<li>If the average number of minutes used each month is 1,160, we have the following:\n<div>[latex]\\begin{array}{l}\\text{Company }A\\hfill&=0.05\\left(1,160\\right)+34\\hfill \\\\ \\hfill&=58+34\\hfill \\\\ \\hfill&=92\\hfill \\\\ \\hfill \\\\ \\text{Company }B\\hfill&=0.04\\left(1,160\\right)+40\\hfill \\\\ \\hfill&=46.4+40\\hfill \\\\ \\hfill&=86.4\\hfill \\end{array}[\/latex]<\/div>\n<p>So, Company <em>B<\/em> offers the lower monthly cost of $86.40 as compared with the $92 monthly cost offered by Company <em>A<\/em> when the average number of minutes used each month is 1,160.<\/li>\n<li>If the average number of minutes used each month is 420, we have the following:\n<div>[latex]\\begin{array}{l}\\text{Company }A\\hfill&=0.05\\left(420\\right)+34\\hfill \\\\ \\hfill&=21+34\\hfill \\\\ \\hfill&=55\\hfill \\\\ \\hfill \\\\ \\text{Company }B\\hfill&=0.04\\left(420\\right)+40\\hfill \\\\ \\hfill&=16.8+40\\hfill \\\\ \\hfill&=56.8\\hfill \\end{array}[\/latex]<\/div>\n<p>If the average number of minutes used each month is 420, then Company <em>A <\/em>offers a lower monthly cost of $55 compared to Company <em>B<\/em>\u2019s monthly cost of $56.80.<\/li>\n<li>To answer the question of how many talk-time minutes would yield the same bill from both companies, we should think about the problem in terms of [latex]\\left(x,y\\right)[\/latex] coordinates: At what point are both the <em>x-<\/em>value and the <em>y-<\/em>value equal? We can find this point by setting the equations equal to each other and solving for <em>x.<\/em>\n<div style=\"text-align: center\">[latex]\\begin{array}{l}0.05x+34=0.04x+40\\hfill \\\\ 0.01x=6\\hfill \\\\ x=600\\hfill \\end{array}[\/latex]<\/div>\n<p>Check the <em>x-<\/em>value in each equation.<\/p>\n<div style=\"text-align: left\">[latex]\\begin{array}{l}0.05\\left(600\\right)+34=64\\hfill \\\\ 0.04\\left(600\\right)+40=64\\hfill \\end{array}[\/latex]<\/div>\n<p>Therefore, a monthly average of 600 talk-time minutes renders the plans equal.<\/li>\n<\/ol>\n<ol>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/09\/25200339\/CNX_CAT_Figure_02_03_002.jpg\" alt=\"Coordinate plane with the x-axis ranging from 0 to 1200 in intervals of 100 and the y-axis ranging from 0 to 90 in intervals of 10. The functions A = 0.05x + 34 and B = 0.04x + 40 are graphed on the same plot\" width=\"731\" height=\"420\" \/>\n<\/div>\n<\/div>\n<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Find a linear equation to model this real-world application: It costs ABC electronics company $2.50 per unit to produce a part used in a popular brand of desktop computers. The company has monthly operating expenses of $350 for utilities and $3,300 for salaries. What are the company\u2019s monthly expenses?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q68149\">Show Show Solution<\/span><\/p>\n<div id=\"q68149\" class=\"hidden-answer\" style=\"display: none\">[latex]C=2.5x+3,650[\/latex]<\/div>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"mom1\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=92426&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"500\"><\/iframe><\/p>\n<\/div>\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-2619\">\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>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>College Algebra. <strong>Authored by<\/strong>: Abramson, Jay et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/a>. <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\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/li><li>Question ID 7647. <strong>Authored by<\/strong>: Tyler Wallace. <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><li>Question ID 30987, 13665. <strong>Authored by<\/strong>: James Sousa. <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><li>Question ID 92426. <strong>Authored by<\/strong>: Michael Jenck. <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\">All rights reserved content<\/div><ul class=\"citation-list\"><li>Learn Desmos: Change Graph Settings. <strong>Authored by<\/strong>: Desmos. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/En_PkyA-4_4\">https:\/\/youtu.be\/En_PkyA-4_4<\/a>. <strong>License<\/strong>: <em>All Rights Reserved<\/em>. <strong>License Terms<\/strong>: Standard YouTube Licesnse<\/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":21,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"College Algebra\",\"author\":\"Abramson, Jay et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at 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