Mrs Fabian had a sum of money. If she bought 4 mini cupcakes and 7 lollipops, she would have $56 left. If she bought 2 mini cupcakes and 9 lollipops, she would have $54 left. Given that she had $85, how many mini cupcakes could she buy at most?
Cost of 1 mini cupcake = 1 M
Cost of 1 lollipop = 1 L

4 M + 7 L + 56 = 85
4 M + 7 L = 85 - 56
4 M + 7 L = 29 ---- (1)

2 M + 9 L + 54 = 85
2 M + 9 L = 85 - 54 
2 M + 9 L = 31 ---- (2)

Make L the same.

(1) _{x 9}
36 M + 63 L = 261 ---- (3)

(2) _{x 7}
14 M + 63 L = 217 ---- (4)

(3) - (4) 
36 M - 14 M = 261 - 217
22 M = 44

1 M = 44 ÷ 22 = 2

Number of mini cupcakes that Mrs Fabian can buy
= 85 ÷ 2
= 42 r 1

Most number of mini cupcakes that Mrs Fabian can buy = 42

Answer(s): 42