Zeph had a sum of money. If he bought 5 shortbreads and 7 puffs, he would be short of $3. If he bought 2 shortbreads and 4 puffs, he would have $18 left. Given that he had $34, how many puffs could he buy at most?
Cost of 1 shortbread = 1 S
Cost of 1 puff = 1 P

5 S + 7 P - 3 = 34
5 S + 7 P = 34 + 3 
5 S + 7 P = 37 --- (1)

2 S + 4 P + 18 = 34 
2 S + 4 P = 34 - 18 
2 S + 4 P = 16 --- (2)

Make S the same.

(1) _{x 2}
10 S + 14 P = 74 
10 S = 74 - 14 P ---- (3)

(2) _{x 5}
10 S + 20 P = 80 
10 S = 80 - 20 P ---- (4)

(3) = (4)
74 - 14 P = 80 - 20 P 
20 P - 14 P = 80 - 74 
6 P = 6

1 P = 6 ÷ 6 = 1 

Cost of 1 puff = $1 

Number of puffs that Zeph can buy at most
= 34 ÷ 1
= 34 r 0

Most number of puffs that Zeph can buy = 34

Answer(s): 34