Vaidev had a sum of money. If he bought 7 scones and 6 puffs, he would be short of $5. If he bought 3 scones and 4 puffs, he would have $31 left. Given that he had $73, how many puffs could he buy at most?
Cost of 1 scone = 1 S
Cost of 1 puff = 1 P

7 S + 6 P - 5 = 73
7 S + 6 P = 73 + 5 
7 S + 6 P = 78 --- (1)

3 S + 4 P + 31 = 73 
3 S + 4 P = 73 - 31 
3 S + 4 P = 42 --- (2)

Make S the same.

(1) _{x 3}
21 S + 18 P = 234 
21 S = 234 - 18 P ---- (3)

(2) _{x 7}
21 S + 28 P = 294 
21 S = 294 - 28 P ---- (4)

(3) = (4)
234 - 18 P = 294 - 28 P 
28 P - 18 P = 294 - 234 
10 P = 60

1 P = 60 ÷ 10 = 6 

Cost of 1 puff = $6 

Number of puffs that Vaidev can buy at most
= 73 ÷ 6
= 12 r 1

Most number of puffs that Vaidev can buy = 12

Answer(s): 12