Mrs Tom had a sum of money. If she bought 5 mini cupcakes and 7 chocolate bars, she would have $41 left. If she bought 2 mini cupcakes and 5 chocolate bars, she would have $53 left. Given that she had $72, how many mini cupcakes could she buy at most?
Cost of 1 mini cupcake = 1 M
Cost of 1 chocolate bar = 1 C

5 M + 7 C + 41 = 72
5 M + 7 C = 72 - 41
5 M + 7 C = 31 ---- (1)

2 M + 5 C + 53 = 72
2 M + 5 C = 72 - 53 
2 M + 5 C = 19 ---- (2)

Make C the same.

(1) _{x 5}
25 M + 35 C = 155 ---- (3)

(2) _{x 7}
14 M + 35 C = 133 ---- (4)

(3) - (4) 
25 M - 14 M = 155 - 133
11 M = 22

1 M = 22 ÷ 11 = 2

Number of mini cupcakes that Mrs Tom can buy
= 72 ÷ 2
= 36 r 0

Most number of mini cupcakes that Mrs Tom can buy = 36

Answer(s): 36