# Welcome to Algebra I: Solving Real-World Problems Involving Systems of Linear Equations

34 minutes

Hey, guys. Welcome to Algebra 1. Today's lesson's going to focus on solving real-world problems involving systems of linear equation. All the practice that you've had solving systems of equations and real-world problems will come in handy in this lesson. You ready? Let's go.

(Describer) She uses a stylus on a screen.

(Describer) She uses a stylus on a screen.

(Describer) She uses a stylus on a screen.

Okay. Before we begin solving systems of equations that deal with real-world problems, let's just jump back and review real-world problems in general. If you look at this problem, I won't solve it, but I'll review the process to solve it, just to jog your memory. "Mateo's monthly cable subscription is \$80. "As part of his service, "he can order newly released movies to view at home "at a cost of \$6 per movie. "Mateo was charged \$104 for his first month of service. How many movies did he order?" If you remember how we've solved this kind of equation, we would read through it, and then go back and highlight anything that sounded like math-- anything that helps us focus on the information we need to set up this equation and solve for the unknown. For example, "His cable subscription's \$80." Sounds like math, it's a number. "As part of his service, "he can order newly released movies to view at home at a cost of \$6 per movie." Let's get that. "Mateo was charged \$104 for his first month of service." Then "how many movies did he order?" The question we're trying to answer. We'd get this information, we'd set up an equation. I'll switch to my pen. So \$80, plus \$6 per movie, if I let X represent the number of movies.

(Describer) She writes 6x.

(Describer) She writes 6x.

(Describer) She writes 6x.

(Describer) X plus y equals 150.

(Describer) X plus y equals 150.

(Describer) X plus y equals 150.

(Describer) Titles: Kelsey is working two part-time jobs this summer to save money to purchase a car. She works at a computer repair store where she earns 15 dollars per hour, and at a clothing store where she earns 12 dollars per hour. Kelsey worked a total of 60 hours last week and earned 825 dollars. How many hours did Kelsey work at each part-time job?

(Describer) Titles: Kelsey is working two part-time jobs this summer to save money to purchase a car. She works at a computer repair store where she earns 15 dollars per hour, and at a clothing store where she earns 12 dollars per hour. Kelsey worked a total of 60 hours last week and earned 825 dollars. How many hours did Kelsey work at each part-time job?

(Describer) Titles: Kelsey is working two part-time jobs this summer to save money to purchase a car. She works at a computer repair store where she earns 15 dollars per hour, and at a clothing store where she earns 12 dollars per hour. Kelsey worked a total of 60 hours last week and earned 825 dollars. How many hours did Kelsey work at each part-time job?

(female narrator) Kelsey is working two part-time jobs this summer to save money to purchase a car. She works at a computer repair store where she earns \$15 per hour, and at a clothing store where she earns \$12 per hour. Kelsey worked 60 hours last week and earned \$825. How many hours did Kelsey work at each part-time job? All right, let's see how you did. I do believe I have the answer here. I'll show you what I got and then do the work. Let's get this out of the way. So Kelsey worked 35 hours at the computer repair store, and 25 hours at the clothing store. If you want to see how I got that answer, watch me do this. I do believe-- nope, I didn't. Let's read it first, and then go back and highlight all of our key information. "Kelsey is working two part-time jobs this summer "to save money to purchase a car. "She works at a computer repair store "where she earns \$15 per hour, and at a clothing store "where she earns \$12 per hour. "Kelsey worked 60 hours total last week and earned \$825. How many hours did Kelsey work at each part-time job?" We read through it once, now let's go back and let's highlight all that important information. Let me switch to my highlighter. So Kelsey is working two part-time jobs this summer to save money to purchase a car. She works at a computer repair store where she earns \$15 an hour. So at the computer repair store, \$15 per hour. And at a clothing store where she earns \$12 per hour. So clothing store, \$12 per hour. "Kelsey worked a total of 60 hours last week "and she earned \$825. How many hours did Kelsey work at each part-time job?" So let's go through this. Computer repair store, \$15 an hour. Clothing store, \$12 an hour. She worked 60 hours, she earned \$825. We're trying to figure out-- I forgot to highlight that-- how many hours she worked at each job. Let's switch to the pen and see if you took these steps to solve this. I'm going to let X represent the hours at the computer store and let Y represent the hours at the clothing store. You could've reversed that; either way is fine. Let's get that answer out of my way so I can work down there. So we're going to let X... Switch to the pen, there we go. X is the computer store-- I'll abbreviate that for computer-- and Y is the clothing store. We're doing a lot of scrolling on this one. And Y is the clothing store. So scroll back up. At the computer repair store she earns \$15 per hour, and at the clothing store she earns \$12 per hour. So I'm going to say 15X... plus 12Y equals 825. That'll handle the money that she's earning. And she worked a total of 60 hours last week. So the hours at the computer store plus the hours at the clothing store were 60. That should've been your system. Your system should've resembled something like this.

(Describer) 15x plus 12y equals 825, and x plus y equals 60.

(Describer) 15x plus 12y equals 825, and x plus y equals 60.

(Describer) 15x plus 12y equals 825, and x plus y equals 60.

Let's get some more workspace, do a little maneuvering up here. We can actually keep that right there. Step 1: I'm going to keep using the substitution method on these. So I'm going to take that second equation and solve it for Y again. So X plus Y equals 60. Subtract X from both sides. So Y equals negative X plus 60. So I have that second equation solved for Y, which will help me to be able to substitute back into that first equation, okay? All right, I'm going to get right underneath this one here. So that first equation is 15X plus 12Y equals 825. So 15 X plus 12Y equals 825, okay? And we'd already solved that second one, so we're going to substitute that negative X plus 60 into this equation for Y. So 15X plus 12 times negative X plus 60 equals 825. Let's get some more space up here. Let's clean this up. Let's bring down the 15X. 12 times negative X. That's negative 12X. 12 times 60. Just to be safe, let's get the calculator on that one. So 12 times 60. 720. Let's go back to our work here. Let's move that out of the way. So plus 720 equals 825. Let's get some more workspace. We can combine these two like terms in the front, So 15X minus 12X, that's 3X. Plus 720 equals 825. Okay? We're trying to get that 3X by itself, so let's subtract 720 from both sides. Let's get a little more workspace. Getting ahead of myself here. So that's going to cancel out, 720 minus 720. There we go. So let's bring down the 3X. 825 minus 720. That's 105. Then our last step: divide each side by three. I'll use calculator for that: 105 divided by 3. Just to make sure that's right. So 105 divided by 3. 35. Let's go back to our work. And we have X equals 35. Let's go back up to the problem to see what meaning that has in relation to the word problem. So if X is 35, and we said that X represented the number of hours she worked at the computer store, then we know that she worked 35 hours at the computer store. Let's write that down. Kind of crowded up here so let's go back to the bottom and write that down. So she worked 35 hours... at the computer store. And if we go back to the problem, I believe it said that she worked a total of 60 hours. Right, so she worked a total of 60 hours. Let's see how many hours are left over for her job at the clothing store. Let's scroll back down. So 60 minus 35. Let's get a little more space here. And that's actually 25. So she worked 35 hours at the computer store, and she worked 25 hours at the clothing store. Your work should have been something similar to that when you were solving that real-world problem. I hope you're feeling confident about how to solve real-world problems involving systems of linear equations. See you back here soon for some more Algebra 1. Bye!

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In this program, students will learn about concepts involving inequalities and systems of equations. These can be used to solve linear programming application problems. Part of the "Welcome to Algebra I" series.

## Media Details

Runtime: 34 minutes

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