Owen had a sum of money. If he bought 7 macarons and 5 puffs, he would be short of $4. If he bought 2 macarons and 3 puffs, he would have $32 left. Given that he had $53, how many puffs could he buy at most?
Cost of 1 macaron = 1 M
Cost of 1 puff = 1 P

7 M + 5 P - 4 = 53
7 M + 5 P = 53 + 4 
7 M + 5 P = 57 --- (1)

2 M + 3 P + 32 = 53 
2 M + 3 P = 53 - 32 
2 M + 3 P = 21 --- (2)

Make M the same.

(1) _{x 2}
14 M + 10 P = 114 
14 M = 114 - 10 P ---- (3)

(2) _{x 7}
14 M + 21 P = 147 
14 M = 147 - 21 P ---- (4)

(3) = (4)
114 - 10 P = 147 - 21 P 
21 P - 10 P = 147 - 114 
11 P = 33

1 P = 33 ÷ 11 = 3 

Cost of 1 puff = $3 

Number of puffs that Owen can buy at most
= 53 ÷ 3
= 17 r 2

Most number of puffs that Owen can buy = 17

Answer(s): 17