Tom had a sum of money. If he bought 5 biscuits and 7 tarts, he would be short of $3. If he bought 2 biscuits and 4 tarts, he would have $33 left. Given that he had $69, how many tarts could he buy at most?
Cost of 1 biscuit = 1 B
Cost of 1 tart = 1 T

5 B + 7 T - 3 = 69
5 B + 7 T = 69 + 3 
5 B + 7 T = 72 --- (1)

2 B + 4 T + 33 = 69 
2 B + 4 T = 69 - 33 
2 B + 4 T = 36 --- (2)

Make B the same.

(1) _{x 2}
10 B + 14 T = 144 
10 B = 144 - 14 T ---- (3)

(2) _{x 5}
10 B + 20 T = 180 
10 B = 180 - 20 T ---- (4)

(3) = (4)
144 - 14 T = 180 - 20 T 
20 T - 14 T = 180 - 144 
6 T = 36

1 T = 36 ÷ 6 = 6 

Cost of 1 tart = $6 

Number of tarts that Tom can buy at most
= 69 ÷ 6
= 11 r 3

Most number of tarts that Tom can buy = 11

Answer(s): 11