Warren had a sum of money. If he bought 7 macarons and 8 cookies, he would be short of $7. If he bought 3 macarons and 4 cookies, he would have $17 left. Given that he had $38, how many cookies could he buy at most?
Cost of 1 macaron = 1 M
Cost of 1 cookie = 1 C

7 M + 8 C - 7 = 38
7 M + 8 C = 38 + 7 
7 M + 8 C = 45 --- (1)

3 M + 4 C + 17 = 38 
3 M + 4 C = 38 - 17 
3 M + 4 C = 21 --- (2)

Make M the same.

(1) _{x 3}
21 M + 24 C = 135 
21 M = 135 - 24 C ---- (3)

(2) _{x 7}
21 M + 28 C = 147 
21 M = 147 - 28 C ---- (4)

(3) = (4)
135 - 24 C = 147 - 28 C 
28 C - 24 C = 147 - 135 
4 C = 12

1 C = 12 ÷ 4 = 3 

Cost of 1 cookie = $3 

Number of cookies that Warren can buy at most
= 38 ÷ 3
= 12 r 2

Most number of cookies that Warren can buy = 12

Answer(s): 12