Mrs Ben had a sum of money. If she bought 4 mini cupcakes and 7 caramel apples, she would have $23 left. If she bought 4 mini cupcakes and 8 caramel apples, she would have $19 left. Given that she had $63, how many mini cupcakes could she buy at most?
Cost of 1 mini cupcake = 1 M
Cost of 1 caramel apple = 1 C

4 M + 7 C + 23 = 63
4 M + 7 C = 63 - 23
4 M + 7 C = 40 ---- (1)

4 M + 8 C + 19 = 63
4 M + 8 C = 63 - 19 
4 M + 8 C = 44 ---- (2)

Make C the same.

(1) _{x 8}
32 M + 56 C = 320 ---- (3)

(2) _{x 7}
28 M + 56 C = 308 ---- (4)

(3) - (4) 
32 M - 28 M = 320 - 308
4 M = 12

1 M = 12 ÷ 4 = 3

Number of mini cupcakes that Mrs Ben can buy
= 63 ÷ 3
= 21 r 0

Most number of mini cupcakes that Mrs Ben can buy = 21

Answer(s): 21