Tommy had a sum of money. If he bought 7 puffs and 6 shortbreads, he would be short of $6. If he bought 4 puffs and 5 shortbreads, he would have $2 left. Given that he had $31, how many shortbreads could he buy at most?
Cost of 1 puff = 1 P
Cost of 1 shortbread = 1 S

7 P + 6 S - 6 = 31
7 P + 6 S = 31 + 6 
7 P + 6 S = 37 --- (1)

4 P + 5 S + 2 = 31 
4 P + 5 S = 31 - 2 
4 P + 5 S = 29 --- (2)

Make P the same.

(1) _{x 4}
28 P + 24 S = 148 
28 P = 148 - 24 S ---- (3)

(2) _{x 7}
28 P + 35 S = 203 
28 P = 203 - 35 S ---- (4)

(3) = (4)
148 - 24 S = 203 - 35 S 
35 S - 24 S = 203 - 148 
11 S = 55

1 S = 55 ÷ 11 = 5 

Cost of 1 shortbread = $5 

Number of shortbreads that Tommy can buy at most
= 31 ÷ 5
= 6 r 1

Most number of shortbreads that Tommy can buy = 6

Answer(s): 6