Ivan had a sum of money. If he bought 5 cookies and 8 tarts, he would be short of $23. If he bought 2 cookies and 4 tarts, he would have $7 left. Given that he had $31, how many tarts could he buy at most?
Cost of 1 cookie = 1 C
Cost of 1 tart = 1 T

5 C + 8 T - 23 = 31
5 C + 8 T = 31 + 23 
5 C + 8 T = 54 --- (1)

2 C + 4 T + 7 = 31 
2 C + 4 T = 31 - 7 
2 C + 4 T = 24 --- (2)

Make C the same.

(1) _{x 2}
10 C + 16 T = 108 
10 C = 108 - 16 T ---- (3)

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

(3) = (4)
108 - 16 T = 120 - 20 T 
20 T - 16 T = 120 - 108 
4 T = 12

1 T = 12 ÷ 4 = 3 

Cost of 1 tart = $3 

Number of tarts that Ivan can buy at most
= 31 ÷ 3
= 10 r 1

Most number of tarts that Ivan can buy = 10

Answer(s): 10