Japheth had a sum of money. If he bought 5 biscuits and 8 tarts, he would be short of $13. If he bought 2 biscuits and 4 tarts, he would have $15 left. Given that he had $39, how many tarts could he buy at most?
Cost of 1 biscuit = 1 B
Cost of 1 tart = 1 T

5 B + 8 T - 13 = 39
5 B + 8 T = 39 + 13 
5 B + 8 T = 52 --- (1)

2 B + 4 T + 15 = 39 
2 B + 4 T = 39 - 15 
2 B + 4 T = 24 --- (2)

Make B the same.

(1) _{x 2}
10 B + 16 T = 104 
10 B = 104 - 16 T ---- (3)

(2) _{x 5}
10 B + 20 T = 120 
10 B = 120 - 20 T ---- (4)

(3) = (4)
104 - 16 T = 120 - 20 T 
20 T - 16 T = 120 - 104 
4 T = 16

1 T = 16 ÷ 4 = 4 

Cost of 1 tart = $4 

Number of tarts that Japheth can buy at most
= 39 ÷ 4
= 9 r 3

Most number of tarts that Japheth can buy = 9

Answer(s): 9