Mrs Neave had a sum of money. If she bought 5 caramel apples and 8 mochi balls, she would have $17 left. If she bought 4 caramel apples and 10 mochi balls, she would have $14 left. Given that she had $74, how many caramel apples could she buy at most?
Cost of 1 caramel apple = 1 C
Cost of 1 mochi ball = 1 M

5 C + 8 M + 17 = 74
5 C + 8 M = 74 - 17
5 C + 8 M = 57 ---- (1)

4 C + 10 M + 14 = 74
4 C + 10 M = 74 - 14 
4 C + 10 M = 60 ---- (2)

Make M the same.

(1) _{x 5}
25 C + 40 M = 285 ---- (3)

(2) _{x 4}
16 C + 40 M = 240 ---- (4)

(3) - (4) 
25 C - 16 C = 285 - 240
9 C = 45

1 C = 45 ÷ 9 = 5

Number of caramel apples that Mrs Neave can buy
= 74 ÷ 5
= 14 r 4

Most number of caramel apples that Mrs Neave can buy = 14

Answer(s): 14