Mrs George had a sum of money. If she bought 2 mini cupcakes and 7 chocolate bars, she would have $5 left. If she bought 2 mini cupcakes and 8 chocolate bars, she would have $3 left. Given that she had $31, how many mini cupcakes could she buy at most?
Cost of 1 mini cupcake = 1 M
Cost of 1 chocolate bar = 1 C

2 M + 7 C + 5 = 31
2 M + 7 C = 31 - 5
2 M + 7 C = 26 ---- (1)

2 M + 8 C + 3 = 31
2 M + 8 C = 31 - 3 
2 M + 8 C = 28 ---- (2)

Make C the same.

(1) _{x 8}
16 M + 56 C = 208 ---- (3)

(2) _{x 7}
14 M + 56 C = 196 ---- (4)

(3) - (4) 
16 M - 14 M = 208 - 196
2 M = 12

1 M = 12 ÷ 2 = 6

Number of mini cupcakes that Mrs George can buy
= 31 ÷ 6
= 5 r 1

Most number of mini cupcakes that Mrs George can buy = 5

Answer(s): 5