Mrs Howard had a sum of money. If she bought 3 mini cupcakes and 7 candy canes, she would have $36 left. If she bought 2 mini cupcakes and 10 candy canes, she would have $33 left. Given that she had $75, how many mini cupcakes could she buy at most?
Cost of 1 mini cupcake = 1 M
Cost of 1 candy cane = 1 C

3 M + 7 C + 36 = 75
3 M + 7 C = 75 - 36
3 M + 7 C = 39 ---- (1)

2 M + 10 C + 33 = 75
2 M + 10 C = 75 - 33 
2 M + 10 C = 42 ---- (2)

Make C the same.

(1) _{x 10}
30 M + 70 C = 390 ---- (3)

(2) _{x 7}
14 M + 70 C = 294 ---- (4)

(3) - (4) 
30 M - 14 M = 390 - 294
16 M = 96

1 M = 96 ÷ 16 = 6

Number of mini cupcakes that Mrs Howard can buy
= 75 ÷ 6
= 12 r 3

Most number of mini cupcakes that Mrs Howard can buy = 12

Answer(s): 12