Mrs Dylan had a sum of money. If she bought 5 mini cupcakes and 8 sweets, she would have $42 left. If she bought 2 mini cupcakes and 9 sweets, she would have $55 left. Given that she had $83, how many mini cupcakes could she buy at most?
Cost of 1 mini cupcake = 1 M
Cost of 1 sweet = 1 S

5 M + 8 S + 42 = 83
5 M + 8 S = 83 - 42
5 M + 8 S = 41 ---- (1)

2 M + 9 S + 55 = 83
2 M + 9 S = 83 - 55 
2 M + 9 S = 28 ---- (2)

Make S the same.

(1) _{x 9}
45 M + 72 S = 369 ---- (3)

(2) _{x 8}
16 M + 72 S = 224 ---- (4)

(3) - (4) 
45 M - 16 M = 369 - 224
29 M = 145

1 M = 145 ÷ 29 = 5

Number of mini cupcakes that Mrs Dylan can buy
= 83 ÷ 5
= 16 r 3

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

Answer(s): 16