Mrs Andy had a sum of money. If she bought 3 mini cupcakes and 7 sweets, she would have $5 left. If she bought 2 mini cupcakes and 10 sweets, she would have $5 left. Given that she had $37, how many mini cupcakes could she buy at most?
Cost of 1 mini cupcake = 1 M
Cost of 1 sweet = 1 S

3 M + 7 S + 5 = 37
3 M + 7 S = 37 - 5
3 M + 7 S = 32 ---- (1)

2 M + 10 S + 5 = 37
2 M + 10 S = 37 - 5 
2 M + 10 S = 32 ---- (2)

Make S the same.

(1) _{x 10}
30 M + 70 S = 320 ---- (3)

(2) _{x 7}
14 M + 70 S = 224 ---- (4)

(3) - (4) 
30 M - 14 M = 320 - 224
16 M = 96

1 M = 96 ÷ 16 = 6

Number of mini cupcakes that Mrs Andy can buy
= 37 ÷ 6
= 6 r 1

Most number of mini cupcakes that Mrs Andy can buy = 6

Answer(s): 6