Mrs Andy had a sum of money. If she bought 5 mochi balls and 8 chocolate bars, she would have $7 left. If she bought 2 mochi balls and 6 chocolate bars, she would have $23 left. Given that she had $43, how many mochi balls could she buy at most?
Cost of 1 mochi ball = 1 M
Cost of 1 chocolate bar = 1 C

5 M + 8 C + 7 = 43
5 M + 8 C = 43 - 7
5 M + 8 C = 36 ---- (1)

2 M + 6 C + 23 = 43
2 M + 6 C = 43 - 23 
2 M + 6 C = 20 ---- (2)

Make C the same.

(1) _{x 3}
15 M + 24 C = 108 ---- (3)

(2) _{x 4}
8 M + 24 C = 80 ---- (4)

(3) - (4) 
15 M - 8 M = 108 - 80
7 M = 28

1 M = 28 ÷ 7 = 4

Number of mochi balls that Mrs Andy can buy
= 43 ÷ 4
= 10 r 3

Most number of mochi balls that Mrs Andy can buy = 10

Answer(s): 10