John had a sum of money. If he bought 7 shortbreads and 8 macarons, he would be short of $4. If he bought 2 shortbreads and 4 macarons, he would have $24 left. Given that he had $40, how many macarons could he buy at most?
Cost of 1 shortbread = 1 S
Cost of 1 macaron = 1 M

7 S + 8 M - 4 = 40
7 S + 8 M = 40 + 4 
7 S + 8 M = 44 --- (1)

2 S + 4 M + 24 = 40 
2 S + 4 M = 40 - 24 
2 S + 4 M = 16 --- (2)

Make S the same.

(1) _{x 2}
14 S + 16 M = 88 
14 S = 88 - 16 M ---- (3)

(2) _{x 7}
14 S + 28 M = 112 
14 S = 112 - 28 M ---- (4)

(3) = (4)
88 - 16 M = 112 - 28 M 
28 M - 16 M = 112 - 88 
12 M = 24

1 M = 24 ÷ 12 = 2 

Cost of 1 macaron = $2 

Number of macarons that John can buy at most
= 40 ÷ 2
= 20 r 0

Most number of macarons that John can buy = 20

Answer(s): 20