2014-10-22 09:00:09

A store sells all T-shirts for $15 and all sweatshirts for $40. Gorgui bought 9 shirts at the store and spent a total of $285 on them. How many MORE sweatshirts did he buy than t-shirts?

(A) 1
(B) 3
(C) 4
(D) 6
(E) 8

The correct answer is B
Explanation: Set up two equations to solve this, letting T be the number of T-shirts Gorgui bought and S be the number of sweatshirts he bought. One equation will represent the total amount he spent, the other the number of shirts he bought:

15T + 40S = 285
T + S = 9

Solve for S in the second equation by subtracting T from both sides, leaving S = 9 - T. Now, substitute that expression in for S in the top equation:

15T + 40(9 - T) = 285.

Distribute the 40 to get 15 T + 360 - 40T = 285, or 360 - 25T = 285.

Subtract 360 from both sides to get -25T = -75. Divide both sides by -25 to get T = 3. Thus, Gorgui bought 3 T-shirts.

Use 3 for T in the second equation from above: T + S = 9 to get (3) + S = 9, meaning S = 6. Thus, he bought 6 sweatshirts. Since the question asks for how many more sweatshirts Gorgui bought than T-shirts, the answer is 6 - 3, or 3, making B correct.