Mrs Xavier had a sum of money. If she bought 4 mochi balls and 7 sweets, she would have $13 left. If she bought 2 mochi balls and 8 sweets, she would have $15 left. Given that she had $71, how many mochi balls could she buy at most?
Cost of 1 mochi ball = 1 M
Cost of 1 sweet = 1 S

4 M + 7 S + 13 = 71
4 M + 7 S = 71 - 13
4 M + 7 S = 58 ---- (1)

2 M + 8 S + 15 = 71
2 M + 8 S = 71 - 15 
2 M + 8 S = 56 ---- (2)

Make S the same.

(1) _{x 8}
32 M + 56 S = 464 ---- (3)

(2) _{x 7}
14 M + 56 S = 392 ---- (4)

(3) - (4) 
32 M - 14 M = 464 - 392
18 M = 72

1 M = 72 ÷ 18 = 4

Number of mochi balls that Mrs Xavier can buy
= 71 ÷ 4
= 17 r 3

Most number of mochi balls that Mrs Xavier can buy = 17

Answer(s): 17