Mrs Vincent had a sum of money. If she bought 5 caramel apples and 7 mochi balls, she would have $68 left. If she bought 4 caramel apples and 6 mochi balls, she would have $73 left. Given that she had $99, 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 + 7 M + 68 = 99
5 C + 7 M = 99 - 68
5 C + 7 M = 31 ---- (1)

4 C + 6 M + 73 = 99
4 C + 6 M = 99 - 73 
4 C + 6 M = 26 ---- (2)

Make M the same.

(1) _{x 6}
30 C + 42 M = 186 ---- (3)

(2) _{x 7}
28 C + 42 M = 182 ---- (4)

(3) - (4) 
30 C - 28 C = 186 - 182
2 C = 4

1 C = 4 ÷ 2 = 2

Number of caramel apples that Mrs Vincent can buy
= 99 ÷ 2
= 49 r 1

Most number of caramel apples that Mrs Vincent can buy = 49

Answer(s): 49