Rael had a sum of money. If he bought 5 scones and 8 wafers, he would be short of $7. If he bought 2 scones and 4 wafers, he would have $31 left. Given that he had $63, how many wafers could he buy at most?
Cost of 1 scone = 1 S
Cost of 1 wafer = 1 W

5 S + 8 W - 7 = 63
5 S + 8 W = 63 + 7 
5 S + 8 W = 70 --- (1)

2 S + 4 W + 31 = 63 
2 S + 4 W = 63 - 31 
2 S + 4 W = 32 --- (2)

Make S the same.

(1) _{x 2}
10 S + 16 W = 140 
10 S = 140 - 16 W ---- (3)

(2) _{x 5}
10 S + 20 W = 160 
10 S = 160 - 20 W ---- (4)

(3) = (4)
140 - 16 W = 160 - 20 W 
20 W - 16 W = 160 - 140 
4 W = 20

1 W = 20 ÷ 4 = 5 

Cost of 1 wafer = $5 

Number of wafers that Rael can buy at most
= 63 ÷ 5
= 12 r 3

Most number of wafers that Rael can buy = 12

Answer(s): 12