Bobby had a sum of money. If he bought 7 shortbreads and 8 puffs, he would be short of $41. If he bought 2 shortbreads and 4 puffs, he would have $3 left. Given that he had $35, how many puffs could he buy at most?
Cost of 1 shortbread = 1 S
Cost of 1 puff = 1 P

7 S + 8 P - 41 = 35
7 S + 8 P = 35 + 41 
7 S + 8 P = 76 --- (1)

2 S + 4 P + 3 = 35 
2 S + 4 P = 35 - 3 
2 S + 4 P = 32 --- (2)

Make S the same.

(1) _{x 2}
14 S + 16 P = 152 
14 S = 152 - 16 P ---- (3)

(2) _{x 7}
14 S + 28 P = 224 
14 S = 224 - 28 P ---- (4)

(3) = (4)
152 - 16 P = 224 - 28 P 
28 P - 16 P = 224 - 152 
12 P = 72

1 P = 72 ÷ 12 = 6 

Cost of 1 puff = $6 

Number of puffs that Bobby can buy at most
= 35 ÷ 6
= 5 r 5

Most number of puffs that Bobby can buy = 5

Answer(s): 5