Glen had a sum of money. If he bought 5 wafers and 6 shortbreads, he would be short of $4. If he bought 2 wafers and 4 shortbreads, he would have $22 left. Given that he had $50, how many shortbreads could he buy at most?
Cost of 1 wafer = 1 W
Cost of 1 shortbread = 1 S

5 W + 6 S - 4 = 50
5 W + 6 S = 50 + 4 
5 W + 6 S = 54 --- (1)

2 W + 4 S + 22 = 50 
2 W + 4 S = 50 - 22 
2 W + 4 S = 28 --- (2)

Make W the same.

(1) _{x 2}
10 W + 12 S = 108 
10 W = 108 - 12 S ---- (3)

(2) _{x 5}
10 W + 20 S = 140 
10 W = 140 - 20 S ---- (4)

(3) = (4)
108 - 12 S = 140 - 20 S 
20 S - 12 S = 140 - 108 
8 S = 32

1 S = 32 ÷ 8 = 4 

Cost of 1 shortbread = $4 

Number of shortbreads that Glen can buy at most
= 50 ÷ 4
= 12 r 2

Most number of shortbreads that Glen can buy = 12

Answer(s): 12