To raise money for new uniforms, the band boosters sell t-shirts and hats. The cost and sale price of each item is shown. The boosters spend a total of $2,000 on T-shirts and hats. They sell all of the merchandise, and make $3375. How many T-shirts did they sell?

Found the problem:

Item Cost Sales Price

T-shirt 6 10

hats 4 7

Let x = t-shirts, y = hats

6x + 4y = 2,000

10x + 7y = 3,375

4y = 2000 - 6x

y = 2000/4 - 6x/4

y = 500 - 3x/2

10x + 7y = 3,375

10x + 7 (500 - 3x/2) = 3,375

10x + 3500 - 21x/2 = 3,375

10x - 10.5x = 3,375 - 3500

-0.5x = - 125

-0.5x / - 0.5 = - 125/-0.5

x = 250 shirts

They will need 250 shirts.