Tom had a sum of money. If he bought 5 macarons and 6 scones, he would be short of $2. If he bought 3 macarons and 4 scones, he would have $14 left. Given that he had $43, how many scones could he buy at most?
Cost of 1 macaron = 1 M
Cost of 1 scone = 1 S

5 M + 6 S - 2 = 43
5 M + 6 S = 43 + 2 
5 M + 6 S = 45 --- (1)

3 M + 4 S + 14 = 43 
3 M + 4 S = 43 - 14 
3 M + 4 S = 29 --- (2)

Make M the same.

(1) _{x 3}
15 M + 18 S = 135 
15 M = 135 - 18 S ---- (3)

(2) _{x 5}
15 M + 20 S = 145 
15 M = 145 - 20 S ---- (4)

(3) = (4)
135 - 18 S = 145 - 20 S 
20 S - 18 S = 145 - 135 
2 S = 10

1 S = 10 ÷ 2 = 5 

Cost of 1 scone = $5 

Number of scones that Tom can buy at most
= 43 ÷ 5
= 8 r 3

Most number of scones that Tom can buy = 8

Answer(s): 8