Harry had a sum of money. If he bought 8 scones and 7 tarts, he would be short of $3. If he bought 3 scones and 4 tarts, he would have $18 left. Given that he had $35, how many tarts could he buy at most?
Cost of 1 scone = 1 S
Cost of 1 tart = 1 T

8 S + 7 T - 3 = 35
8 S + 7 T = 35 + 3 
8 S + 7 T = 38 --- (1)

3 S + 4 T + 18 = 35 
3 S + 4 T = 35 - 18 
3 S + 4 T = 17 --- (2)

Make S the same.

(1) _{x 3}
24 S + 21 T = 114 
24 S = 114 - 21 T ---- (3)

(2) _{x 8}
24 S + 32 T = 136 
24 S = 136 - 32 T ---- (4)

(3) = (4)
114 - 21 T = 136 - 32 T 
32 T - 21 T = 136 - 114 
11 T = 22

1 T = 22 ÷ 11 = 2 

Cost of 1 tart = $2 

Number of tarts that Harry can buy at most
= 35 ÷ 2
= 17 r 1

Most number of tarts that Harry can buy = 17

Answer(s): 17