Question

The Elkhart Athletic Departments sells T-shirts and Hats at a big game to raise money. They sale the T-shirts for $12 and the Hats for $5. At the last football game they sold a total of 32 items and raised $265. How many T-shirts and Hats were sold at the game?

Answer 1

Let x represent the number of T shirts that they sold

Let y represent the number of hats that they sold

They sold the T-shirts for $12 and the Hats for $5. This means that the cost of x T shirts and y hats would be

12 * x + 5 * y

= 12x + 5y

The total amount raised was $265. It means that

12x + 5y = 265 equation 1

Also, the total number of t shirts and hats sold was 32. It means that

x + y = 32

x = 32 - y

Substituting x = 32 - y into equation 1, it becomes

12(32 - y) + 5y = 265

384 - 12y + 5y = 265

- 12y + 5y = 265 - 384

7y = 119

y = 119/7

y = 17

x = 32 - y = 32 - 17

x = 15

15 T shirts and 17 hats