Ben had a sum of money. If he bought 7 tarts and 6 shortbreads, he would be short of $44. If he bought 2 tarts and 3 shortbreads, he would have $4 left. Given that he had $34, how many shortbreads could he buy at most?
Cost of 1 tart = 1 T
Cost of 1 shortbread = 1 S

7 T + 6 S - 44 = 34
7 T + 6 S = 34 + 44 
7 T + 6 S = 78 --- (1)

2 T + 3 S + 4 = 34 
2 T + 3 S = 34 - 4 
2 T + 3 S = 30 --- (2)

Make T the same.

(1) _{x 2}
14 T + 12 S = 156 
14 T = 156 - 12 S ---- (3)

(2) _{x 7}
14 T + 21 S = 210 
14 T = 210 - 21 S ---- (4)

(3) = (4)
156 - 12 S = 210 - 21 S 
21 S - 12 S = 210 - 156 
9 S = 54

1 S = 54 ÷ 9 = 6 

Cost of 1 shortbread = $6 

Number of shortbreads that Ben can buy at most
= 34 ÷ 6
= 5 r 4

Most number of shortbreads that Ben can buy = 5

Answer(s): 5