Wesley had a sum of money. If he bought 7 puffs and 6 macarons, he would be short of $10. If he bought 3 puffs and 4 macarons, he would have $16 left. Given that he had $43, how many macarons could he buy at most?
Cost of 1 puff = 1 P
Cost of 1 macaron = 1 M

7 P + 6 M - 10 = 43
7 P + 6 M = 43 + 10 
7 P + 6 M = 53 --- (1)

3 P + 4 M + 16 = 43 
3 P + 4 M = 43 - 16 
3 P + 4 M = 27 --- (2)

Make P the same.

(1) _{x 3}
21 P + 18 M = 159 
21 P = 159 - 18 M ---- (3)

(2) _{x 7}
21 P + 28 M = 189 
21 P = 189 - 28 M ---- (4)

(3) = (4)
159 - 18 M = 189 - 28 M 
28 M - 18 M = 189 - 159 
10 M = 30

1 M = 30 ÷ 10 = 3 

Cost of 1 macaron = $3 

Number of macarons that Wesley can buy at most
= 43 ÷ 3
= 14 r 1

Most number of macarons that Wesley can buy = 14

Answer(s): 14