Writing a System of Equations

by Maria
(Columbia)

Find the equations to: Alice spent $131 on shoes. Sneakers cost $15 and Fits cost $28. If she bought a total of 7 shoes, then how many of each kind of shoe did she buy?

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Writing a System of Equations

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Oct 22, 2010
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by: Karin

Hi Maria,

With this direction, you are being asked to write a system of equations. You want to write two equations that pertain to this problem.

Notice that you are given two different pieces of information. You are given information about the price of the shoes and the number of shoes bought.
Therefore, we will write one equation for both pieces of information.

First we will define our variables. The information that we don't know is how many of each kind of shoe was purchased.

Let x = Sneakers
Let y = Fits

Our first equation based on price is:
15x + 28y = 131

The second equation based on number is:
x + y = 7

You now have two linear equations based on this one problem. You can solve the system of equations to find out how many of each type of shoe you have.

Hope this helps,
Karin

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