Ben had a sum of money. If he bought 5 puffs and 7 macarons, he would be short of $1. If he bought 2 puffs and 4 macarons, he would have $17 left. Given that he had $33, how many macarons could he buy at most?
Cost of 1 puff = 1 P
Cost of 1 macaron = 1 M

5 P + 7 M - 1 = 33
5 P + 7 M = 33 + 1 
5 P + 7 M = 34 --- (1)

2 P + 4 M + 17 = 33 
2 P + 4 M = 33 - 17 
2 P + 4 M = 16 --- (2)

Make P the same.

(1) _{x 2}
10 P + 14 M = 68 
10 P = 68 - 14 M ---- (3)

(2) _{x 5}
10 P + 20 M = 80 
10 P = 80 - 20 M ---- (4)

(3) = (4)
68 - 14 M = 80 - 20 M 
20 M - 14 M = 80 - 68 
6 M = 12

1 M = 12 ÷ 6 = 2 

Cost of 1 macaron = $2 

Number of macarons that Ben can buy at most
= 33 ÷ 2
= 16 r 1

Most number of macarons that Ben can buy = 16

Answer(s): 16