John had a sum of money. If he bought 8 biscuits and 7 tarts, he would be short of $18. If he bought 3 biscuits and 4 tarts, he would have $16 left. Given that he had $43, how many tarts could he buy at most?
Cost of 1 biscuit = 1 B
Cost of 1 tart = 1 T

8 B + 7 T - 18 = 43
8 B + 7 T = 43 + 18 
8 B + 7 T = 61 --- (1)

3 B + 4 T + 16 = 43 
3 B + 4 T = 43 - 16 
3 B + 4 T = 27 --- (2)

Make B the same.

(1) _{x 3}
24 B + 21 T = 183 
24 B = 183 - 21 T ---- (3)

(2) _{x 8}
24 B + 32 T = 216 
24 B = 216 - 32 T ---- (4)

(3) = (4)
183 - 21 T = 216 - 32 T 
32 T - 21 T = 216 - 183 
11 T = 33

1 T = 33 ÷ 11 = 3 

Cost of 1 tart = $3 

Number of tarts that John can buy at most
= 43 ÷ 3
= 14 r 1

Most number of tarts that John can buy = 14

Answer(s): 14