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## Solving Systems of Equations Word Problems

#### High School - HSA-REI.C.5

What Are Systems of Equations in Math? When you consider systems in mathematics, you are talking about equations and their unknowns. Thus, we must learn the concepts of systems when we are learning algebra. Systems of the equation consist of at least two equations that have similar variables in them. In the concept, the number of equations is directly proportional to the number of variables present in them. Let us take an example which consists of variables x and y. You can communicate these types of problems in algebraic or narrative form. Here is an example of a system of equations :x + y = 6 and -3x + y = 2. Now, we need to solve them simultaneously, to get the values of x and y. When you solve them you will come across a condition. Let us resolve them. x = 6 - y : eq (a)| Here, we will place the value of x in the second equation. -3(6-y) + y = 2 unto -18 + 3y + y = 2 unto 4y = 18 + 2 unto y = 5. Now, we will place the value of y in eq (a). x = 6 - 5 therefore x = 1. The solution set is (1, 5). The condition is that on the graph, both lines will intersect at some point. Your goal by substituting values into the other equation is to locate this point. The best thing about this problem is that it easy to double check your solution. All you need to do is to plug the x and y value of your solution into both equations. If you are correct, they will work for both equations. For the purposes of this topic, we will focus on the narrative form with this topic, but to see it written algebraically is good to get us going. Students will work with systems of equations that can be found within word problems in this problem set. The worksheets and lessons will show students how to setup up these problems.

### Printable Worksheets And Lessons  #### Homework Sheets

Some of these problems were so hard to get right that it took several tries.

• Homework 1 - A test has 20 questions worth a total of 100 points. There are two question types on the test. Matching questions are worth 4 points and multiple choice questions are worth 6 points. How many multiple choice and matching questions are there each?
• Homework 2 - 3 small vases and one large vase hold 6 liters of water. If you poured a full large vase into a small vase and filled it, you would still have 2 liters of water left in the large vase. How much water can a large vase hold?
• Homework 3 - Billy went to the fun park. He rode the water slide 5 times and the Ferris wheel twice. He spent \$20 on the rides. Jenny rode the water slide 3 times and the Ferris wheel 3 times. Jenny spent \$21 on rides. How much does it cost to go on the water slide?

#### Practice Worksheets

The flow here is set up to make students work a little harder as they go along.

• Practice 1 - Shelly wants to make cookies. She has two different sized cooking pans. She only uses one pan per flavor of cookie. On Saturday, she makes 12 pans of chocolate cookies and 10 pans of vanilla cookies for a total of 312 cookies. On Sunday, She makes 5 pans of chocolate cookies and 3 pans of vanilla cookies for a total of 116 cookies.
• Practice 2 - Ash sells dumplings at the local farmer’s market. On Monday, he sold 12 veggie dumplings and 15 meat dumplings for \$69. On Tuesday, he sold 18 veggie dumplings and 7 meat dumplings for \$57.
• Practice 3 - The sum of two numbers is 26. The difference of the same two numbers is 8. What are the numbers?

#### Math Skill Quizzes

The quizzes were hard to get set correctly. It took me a while to get the numbers to balance.

• Quiz 1 - Kelly had a great basketball game today. She made 39 points with 16 different shots. If she only made two and three point shots, how many of each did she make?
• Quiz 2 - At the movies, an adult ticket costs \$9 and a kid’s ticket costs \$6. If Mr. Fluffy brought 9 people and spent \$69, how many kids did he pay for?
• Quiz 3 - A Snickers bar has 150 more calories than a large chocolate chip cookie. Donnie has 3 Snickers bars and 4 chocolate chip cookies for a total of 1,150 calories. How many calories are in each Snickers bar and Chocolate chip cookie?