Question

A baseball coach purchased bats and batting helmets. The coach purchased 19 items in all. Each bat cost $18.25 and each batting helmet cost $24.50. If the coach spent a total of $396.75, how many bats did the coach purchase?

Answer 1

11 bat and 8 helmets.

Explanation:

Let x = the number of bats

Let y = the number of batting helmets

x + y = 19 Rewrite as y = 19 - x

18.25x + 24.50y = 369.75 Multiply by 100

1825x + 2450y = 36975 Substitute 19 - x for y

1825x + 2450(19 -x) = 39675 Distribute the 2450

1825x + 46550 - 2450x = 39675 combine like terms

-625x + 46550 = 39675 subtract 46550 from both sides

-625x = -6875 Divide both sides by -625

x = 11

He bought 11 bats

x + y = 19 Substitute 11 for x to solve for y

11 + y = 19 Subtract 11 from both sides

y = 8

He bought 8 helmets.