George had a sum of money. If he bought 8 muffins and 6 shortbreads, he would be short of $9. If he bought 5 muffins and 4 shortbreads, he would have $7 left. Given that he had $37, how many shortbreads could he buy at most?
Cost of 1 muffin = 1 M
Cost of 1 shortbread = 1 S

8 M + 6 S - 9 = 37
8 M + 6 S = 37 + 9 
8 M + 6 S = 46 --- (1)

5 M + 4 S + 7 = 37 
5 M + 4 S = 37 - 7 
5 M + 4 S = 30 --- (2)

Make M the same.

(1) _{x 5}
40 M + 30 S = 230 
40 M = 230 - 30 S ---- (3)

(2) _{x 8}
40 M + 32 S = 240 
40 M = 240 - 32 S ---- (4)

(3) = (4)
230 - 30 S = 240 - 32 S 
32 S - 30 S = 240 - 230 
2 S = 10

1 S = 10 ÷ 2 = 5 

Cost of 1 shortbread = $5 

Number of shortbreads that George can buy at most
= 37 ÷ 5
= 7 r 2

Most number of shortbreads that George can buy = 7

Answer(s): 7