Mrs Oliver had a sum of money. If she bought 5 caramel apples and 6 mini cupcakes, she would have $8 left. If she bought 3 caramel apples and 9 mini cupcakes, she would have $8 left. Given that she had $35, how many caramel apples could she buy at most?
Cost of 1 caramel apple = 1 C
Cost of 1 mini cupcake = 1 M

5 C + 6 M + 8 = 35
5 C + 6 M = 35 - 8
5 C + 6 M = 27 ---- (1)

3 C + 9 M + 8 = 35
3 C + 9 M = 35 - 8 
3 C + 9 M = 27 ---- (2)

Make M the same.

(1) _{x 3}
15 C + 18 M = 81 ---- (3)

(2) _{x 2}
6 C + 18 M = 54 ---- (4)

(3) - (4) 
15 C - 6 C = 81 - 54
9 C = 27

1 C = 27 ÷ 9 = 3

Number of caramel apples that Mrs Oliver can buy
= 35 ÷ 3
= 11 r 2

Most number of caramel apples that Mrs Oliver can buy = 11

Answer(s): 11