Jeremy had a sum of money. If he bought 7 macarons and 8 scones, he would be short of $47. If he bought 2 macarons and 3 scones, he would have $13 left. Given that he had $43, how many scones could he buy at most?
Cost of 1 macaron = 1 M
Cost of 1 scone = 1 S

7 M + 8 S - 47 = 43
7 M + 8 S = 43 + 47 
7 M + 8 S = 90 --- (1)

2 M + 3 S + 13 = 43 
2 M + 3 S = 43 - 13 
2 M + 3 S = 30 --- (2)

Make M the same.

(1) _{x 2}
14 M + 16 S = 180 
14 M = 180 - 16 S ---- (3)

(2) _{x 7}
14 M + 21 S = 210 
14 M = 210 - 21 S ---- (4)

(3) = (4)
180 - 16 S = 210 - 21 S 
21 S - 16 S = 210 - 180 
5 S = 30

1 S = 30 ÷ 5 = 6 

Cost of 1 scone = $6 

Number of scones that Jeremy can buy at most
= 43 ÷ 6
= 7 r 1

Most number of scones that Jeremy can buy = 7

Answer(s): 7