Ben had a sum of money. If he bought 7 tarts and 8 cupcakes, he would be short of $15. If he bought 2 tarts and 3 cupcakes, he would have $45 left. Given that he had $75, how many cupcakes could he buy at most?
Cost of 1 tart = 1 T
Cost of 1 cupcake = 1 C

7 T + 8 C - 15 = 75
7 T + 8 C = 75 + 15 
7 T + 8 C = 90 --- (1)

2 T + 3 C + 45 = 75 
2 T + 3 C = 75 - 45 
2 T + 3 C = 30 --- (2)

Make T the same.

(1) _{x 2}
14 T + 16 C = 180 
14 T = 180 - 16 C ---- (3)

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

(3) = (4)
180 - 16 C = 210 - 21 C 
21 C - 16 C = 210 - 180 
5 C = 30

1 C = 30 ÷ 5 = 6 

Cost of 1 cupcake = $6 

Number of cupcakes that Ben can buy at most
= 75 ÷ 6
= 12 r 3

Most number of cupcakes that Ben can buy = 12

Answer(s): 12