Luke had a sum of money. If he bought 5 tarts and 8 cupcakes, he would be short of $20. If he bought 2 tarts and 4 cupcakes, he would have $6 left. Given that he had $30, how many cupcakes could he buy at most?
Cost of 1 tart = 1 T
Cost of 1 cupcake = 1 C

5 T + 8 C - 20 = 30
5 T + 8 C = 30 + 20 
5 T + 8 C = 50 --- (1)

2 T + 4 C + 6 = 30 
2 T + 4 C = 30 - 6 
2 T + 4 C = 24 --- (2)

Make T the same.

(1) _{x 2}
10 T + 16 C = 100 
10 T = 100 - 16 C ---- (3)

(2) _{x 5}
10 T + 20 C = 120 
10 T = 120 - 20 C ---- (4)

(3) = (4)
100 - 16 C = 120 - 20 C 
20 C - 16 C = 120 - 100 
4 C = 20

1 C = 20 ÷ 4 = 5 

Cost of 1 cupcake = $5 

Number of cupcakes that Luke can buy at most
= 30 ÷ 5
= 6 r 0

Most number of cupcakes that Luke can buy = 6

Answer(s): 6