Tommy had a sum of money. If he bought 7 tarts and 6 cupcakes, he would be short of $1. If he bought 2 tarts and 3 cupcakes, he would have $22 left. Given that he had $42, how many cupcakes could he buy at most?
Cost of 1 tart = 1 T
Cost of 1 cupcake = 1 C

7 T + 6 C - 1 = 42
7 T + 6 C = 42 + 1 
7 T + 6 C = 43 --- (1)

2 T + 3 C + 22 = 42 
2 T + 3 C = 42 - 22 
2 T + 3 C = 20 --- (2)

Make T the same.

(1) _{x 2}
14 T + 12 C = 86 
14 T = 86 - 12 C ---- (3)

(2) _{x 7}
14 T + 21 C = 140 
14 T = 140 - 21 C ---- (4)

(3) = (4)
86 - 12 C = 140 - 21 C 
21 C - 12 C = 140 - 86 
9 C = 54

1 C = 54 ÷ 9 = 6 

Cost of 1 cupcake = $6 

Number of cupcakes that Tommy can buy at most
= 42 ÷ 6
= 7 r 0

Most number of cupcakes that Tommy can buy = 7

Answer(s): 7