Systems of Equations Story Problem

by Katie
(United States)

Please help with the following problem.

Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of friends purchased 8 tickets for $52.75. Write a system of equations to represent this situation. How many adult tickets and student tickets were purchased?

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Jan 17, 2010
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by: Karin

Hi Katie,

I love systems of equations problems, so I will be happy to help!

A system of equations requires two equations. In this problem, you are given two different pieces of information, one about the price and one about the number of tickets. We will write an equation for each.

Let's first define our variables.
Let x = the number of adult tickets
Let y = the number of student tickets.

Our equation about the price is as follows:

7.25x + 5.50y = 52.75

Our equation about the number of tickets is:
x + y = 8

Those two equations make up your system of equations. Now you need to solve.

I would use the substitution method.

Rewrite x + y = 8 as y = -x +8

Substitute y = -x + 8 into the first equation for y.

7.25x + 5.5(-x + 8) = 52.75

7.25x -5.5x + 44 = 52.75

1.75x + 44 = 52.75

1.75x + 44 -44 = 52.75-44
1.75 x = 8.75

1.75/1.75x = 8.75/1.75

x = 5

x + y = 8

5 + y = 8

y = 3

5 Adult tickets were purchased and 3 student tickets were purchased.

I hope this helps. You can reference the following pages:

Systems Word Problems.

Good luck to you!

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