Mrs Fred had a sum of money. If she bought 2 mini cupcakes and 7 lollipops, she would have $7 left. If she bought 2 mini cupcakes and 9 lollipops, she would have $1 left. Given that she had $32, how many mini cupcakes could she buy at most?
Cost of 1 mini cupcake = 1 M
Cost of 1 lollipop = 1 L

2 M + 7 L + 7 = 32
2 M + 7 L = 32 - 7
2 M + 7 L = 25 ---- (1)

2 M + 9 L + 1 = 32
2 M + 9 L = 32 - 1 
2 M + 9 L = 31 ---- (2)

Make L the same.

(1) _{x 9}
18 M + 63 L = 225 ---- (3)

(2) _{x 7}
14 M + 63 L = 217 ---- (4)

(3) - (4) 
18 M - 14 M = 225 - 217
4 M = 8

1 M = 8 ÷ 4 = 2

Number of mini cupcakes that Mrs Fred can buy
= 32 ÷ 2
= 16 r 0

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

Answer(s): 16