Mrs Ian had a sum of money. If she bought 5 mini cupcakes and 8 caramel apples, she would have $10 left. If she bought 2 mini cupcakes and 6 caramel apples, she would have $22 left. Given that she had $44, how many mini cupcakes could she buy at most?
Cost of 1 mini cupcake = 1 M
Cost of 1 caramel apple = 1 C

5 M + 8 C + 10 = 44
5 M + 8 C = 44 - 10
5 M + 8 C = 34 ---- (1)

2 M + 6 C + 22 = 44
2 M + 6 C = 44 - 22 
2 M + 6 C = 22 ---- (2)

Make C the same.

(1) _{x 3}
15 M + 24 C = 102 ---- (3)

(2) _{x 4}
8 M + 24 C = 88 ---- (4)

(3) - (4) 
15 M - 8 M = 102 - 88
7 M = 14

1 M = 14 ÷ 7 = 2

Number of mini cupcakes that Mrs Ian can buy
= 44 ÷ 2
= 22 r 0

Most number of mini cupcakes that Mrs Ian can buy = 22

Answer(s): 22