Sean had a sum of money. If he bought 7 macarons and 5 shortbreads, he would be short of $14. If he bought 2 macarons and 3 shortbreads, he would have $17 left. Given that he had $36, how many shortbreads could he buy at most?
Cost of 1 macaron = 1 M
Cost of 1 shortbread = 1 S

7 M + 5 S - 14 = 36
7 M + 5 S = 36 + 14 
7 M + 5 S = 50 --- (1)

2 M + 3 S + 17 = 36 
2 M + 3 S = 36 - 17 
2 M + 3 S = 19 --- (2)

Make M the same.

(1) _{x 2}
14 M + 10 S = 100 
14 M = 100 - 10 S ---- (3)

(2) _{x 7}
14 M + 21 S = 133 
14 M = 133 - 21 S ---- (4)

(3) = (4)
100 - 10 S = 133 - 21 S 
21 S - 10 S = 133 - 100 
11 S = 33

1 S = 33 ÷ 11 = 3 

Cost of 1 shortbread = $3 

Number of shortbreads that Sean can buy at most
= 36 ÷ 3
= 12 r 0

Most number of shortbreads that Sean can buy = 12

Answer(s): 12