Billy had a sum of money. If he bought 5 macarons and 6 shortbreads, he would be short of $5. If he bought 2 macarons and 3 shortbreads, he would have $19 left. Given that he had $41, how many shortbreads could he buy at most?
Cost of 1 macaron = 1 M
Cost of 1 shortbread = 1 S

5 M + 6 S - 5 = 41
5 M + 6 S = 41 + 5 
5 M + 6 S = 46 --- (1)

2 M + 3 S + 19 = 41 
2 M + 3 S = 41 - 19 
2 M + 3 S = 22 --- (2)

Make M the same.

(1) _{x 2}
10 M + 12 S = 92 
10 M = 92 - 12 S ---- (3)

(2) _{x 5}
10 M + 15 S = 110 
10 M = 110 - 15 S ---- (4)

(3) = (4)
92 - 12 S = 110 - 15 S 
15 S - 12 S = 110 - 92 
3 S = 18

1 S = 18 ÷ 3 = 6 

Cost of 1 shortbread = $6 

Number of shortbreads that Billy can buy at most
= 41 ÷ 6
= 6 r 5

Most number of shortbreads that Billy can buy = 6

Answer(s): 6