Mrs Riordan had a sum of money. If she bought 5 mochi balls and 6 chocolate bars, she would have $44 left. If she bought 4 mochi balls and 10 chocolate bars, she would have $42 left. Given that she had $86, 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 + 6 C + 44 = 86
5 M + 6 C = 86 - 44
5 M + 6 C = 42 ---- (1)

4 M + 10 C + 42 = 86
4 M + 10 C = 86 - 42 
4 M + 10 C = 44 ---- (2)

Make C the same.

(1) _{x 5}
25 M + 30 C = 210 ---- (3)

(2) _{x 3}
12 M + 30 C = 132 ---- (4)

(3) - (4) 
25 M - 12 M = 210 - 132
13 M = 78

1 M = 78 ÷ 13 = 6

Number of mochi balls that Mrs Riordan can buy
= 86 ÷ 6
= 14 r 2

Most number of mochi balls that Mrs Riordan can buy = 14

Answer(s): 14