ACT Math Test : Solving Systems of Equations in Word Problems

Study concepts, example questions & explanations for ACT Math Test

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Example Questions

Example Question #11 : Word Translations

A sporting good store sells one type of baseball bat and one type of baseball. The cost for 2 bats and 4 balls is $160. The cost for 1 bat and 6 balls is $160, as well. If someone were to buy an equal number of bats and balls, at most how many bats can he purchase if he has a budget of $240 for the purchase?

Possible Answers:

4

6

7

3

5

Correct answer:

4

Explanation:

This word problem starts you off with two equations. If you assign variables as  = bats and  = balls, you have:

, which reduces to 

and

You can then use the Elimination Method to eliminate the  terms and solve for :

, so . Plug that back in, and . So now you have the prices.

At this point, you know that you need the same number of  and , and that the total can only be as high as $240. If you call that same number , you have:

. So you'll be able to buy 4 bats and 4 balls.

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