Ben had a sum of money. If he bought 8 macarons and 7 wafers, he would be short of $15. If he bought 3 macarons and 4 wafers, he would have $20 left. Given that he had $52, how many wafers could he buy at most?
Cost of 1 macaron = 1 M
Cost of 1 wafer = 1 W

8 M + 7 W - 15 = 52
8 M + 7 W = 52 + 15 
8 M + 7 W = 67 --- (1)

3 M + 4 W + 20 = 52 
3 M + 4 W = 52 - 20 
3 M + 4 W = 32 --- (2)

Make M the same.

(1) _{x 3}
24 M + 21 W = 201 
24 M = 201 - 21 W ---- (3)

(2) _{x 8}
24 M + 32 W = 256 
24 M = 256 - 32 W ---- (4)

(3) = (4)
201 - 21 W = 256 - 32 W 
32 W - 21 W = 256 - 201 
11 W = 55

1 W = 55 ÷ 11 = 5 

Cost of 1 wafer = $5 

Number of wafers that Ben can buy at most
= 52 ÷ 5
= 10 r 2

Most number of wafers that Ben can buy = 10

Answer(s): 10