Vaidev had a sum of money. If he bought 5 macarons and 6 tarts, he would be short of $5. If he bought 3 macarons and 4 tarts, he would have $7 left. Given that he had $30, how many tarts could he buy at most?
Cost of 1 macaron = 1 M
Cost of 1 tart = 1 T

5 M + 6 T - 5 = 30
5 M + 6 T = 30 + 5 
5 M + 6 T = 35 --- (1)

3 M + 4 T + 7 = 30 
3 M + 4 T = 30 - 7 
3 M + 4 T = 23 --- (2)

Make M the same.

(1) _{x 3}
15 M + 18 T = 105 
15 M = 105 - 18 T ---- (3)

(2) _{x 5}
15 M + 20 T = 115 
15 M = 115 - 20 T ---- (4)

(3) = (4)
105 - 18 T = 115 - 20 T 
20 T - 18 T = 115 - 105 
2 T = 10

1 T = 10 ÷ 2 = 5 

Cost of 1 tart = $5 

Number of tarts that Vaidev can buy at most
= 30 ÷ 5
= 6 r 0

Most number of tarts that Vaidev can buy = 6

Answer(s): 6