Sample Question

A local baseball team decided to give away hats and bats as promotional items for the first 1,000 fans. The cost to the team is $12 per hat and $8 per bat. The promotional manager would like to use all $10,300 of his budget on this promotion.

Find how many hats and bats should be given away by using a matrix equation.

Sample Response

Let h = the # of hats given away.
Let b = the # of bats given away.

The total hats and bats will always be 1000, so h + b = 1000.
The cost total will be $12 per hat plus $8 per bat, so 12h + 8b = 10300.

The two equations can be rewritten as the matrix equation

Solving with a calculator I'll find .
I get .

So they should give away 575 hats and 425 bats.