Mrs Bryan had a sum of money. If she bought 3 mini cupcakes and 8 chocolate bars, she would have $5 left. If she bought 2 mini cupcakes and 7 chocolate bars, she would have $15 left. Given that she had $65, how many mini cupcakes could she buy at most?
Cost of 1 mini cupcake = 1 M
Cost of 1 chocolate bar = 1 C

3 M + 8 C + 5 = 65
3 M + 8 C = 65 - 5
3 M + 8 C = 60 ---- (1)

2 M + 7 C + 15 = 65
2 M + 7 C = 65 - 15 
2 M + 7 C = 50 ---- (2)

Make C the same.

(1) _{x 7}
21 M + 56 C = 420 ---- (3)

(2) _{x 8}
16 M + 56 C = 400 ---- (4)

(3) - (4) 
21 M - 16 M = 420 - 400
5 M = 20

1 M = 20 ÷ 5 = 4

Number of mini cupcakes that Mrs Bryan can buy
= 65 ÷ 4
= 16 r 1

Most number of mini cupcakes that Mrs Bryan can buy = 16

Answer(s): 16