Mrs Archie had a sum of money. If she bought 5 mochi balls and 8 sweets, she would have $20 left. If she bought 3 mochi balls and 10 sweets, she would have $12 left. Given that she had $78, how many mochi balls could she buy at most?
Cost of 1 mochi ball = 1 M
Cost of 1 sweet = 1 S

5 M + 8 S + 20 = 78
5 M + 8 S = 78 - 20
5 M + 8 S = 58 ---- (1)

3 M + 10 S + 12 = 78
3 M + 10 S = 78 - 12 
3 M + 10 S = 66 ---- (2)

Make S the same.

(1) _{x 5}
25 M + 40 S = 290 ---- (3)

(2) _{x 4}
12 M + 40 S = 264 ---- (4)

(3) - (4) 
25 M - 12 M = 290 - 264
13 M = 26

1 M = 26 ÷ 13 = 2

Number of mochi balls that Mrs Archie can buy
= 78 ÷ 2
= 39 r 0

Most number of mochi balls that Mrs Archie can buy = 39

Answer(s): 39