Ahmad had a sum of money. If he bought 7 tarts and 8 macarons, he would be short of $7. If he bought 3 tarts and 4 macarons, he would have $21 left. Given that he had $46, how many macarons could he buy at most?
Cost of 1 tart = 1 T
Cost of 1 macaron = 1 M

7 T + 8 M - 7 = 46
7 T + 8 M = 46 + 7 
7 T + 8 M = 53 --- (1)

3 T + 4 M + 21 = 46 
3 T + 4 M = 46 - 21 
3 T + 4 M = 25 --- (2)

Make T the same.

(1) _{x 3}
21 T + 24 M = 159 
21 T = 159 - 24 M ---- (3)

(2) _{x 7}
21 T + 28 M = 175 
21 T = 175 - 28 M ---- (4)

(3) = (4)
159 - 24 M = 175 - 28 M 
28 M - 24 M = 175 - 159 
4 M = 16

1 M = 16 ÷ 4 = 4 

Cost of 1 macaron = $4 

Number of macarons that Ahmad can buy at most
= 46 ÷ 4
= 11 r 2

Most number of macarons that Ahmad can buy = 11

Answer(s): 11