Sam had a sum of money. If he bought 7 puffs and 6 shortbreads, he would be short of $4. If he bought 3 puffs and 4 shortbreads, he would have $18 left. Given that he had $37, how many shortbreads could he buy at most?
Cost of 1 puff = 1 P
Cost of 1 shortbread = 1 S

7 P + 6 S - 4 = 37
7 P + 6 S = 37 + 4 
7 P + 6 S = 41 --- (1)

3 P + 4 S + 18 = 37 
3 P + 4 S = 37 - 18 
3 P + 4 S = 19 --- (2)

Make P the same.

(1) _{x 3}
21 P + 18 S = 123 
21 P = 123 - 18 S ---- (3)

(2) _{x 7}
21 P + 28 S = 133 
21 P = 133 - 28 S ---- (4)

(3) = (4)
123 - 18 S = 133 - 28 S 
28 S - 18 S = 133 - 123 
10 S = 10

1 S = 10 ÷ 10 = 1 

Cost of 1 shortbread = $1 

Number of shortbreads that Sam can buy at most
= 37 ÷ 1
= 37 r 0

Most number of shortbreads that Sam can buy = 37

Answer(s): 37