David had a sum of money. If he bought 7 scones and 8 cookies, he would be short of $7. If he bought 2 scones and 4 cookies, he would have $33 left. Given that he had $61, how many cookies could he buy at most?
Cost of 1 scone = 1 S
Cost of 1 cookie = 1 C

7 S + 8 C - 7 = 61
7 S + 8 C = 61 + 7 
7 S + 8 C = 68 --- (1)

2 S + 4 C + 33 = 61 
2 S + 4 C = 61 - 33 
2 S + 4 C = 28 --- (2)

Make S the same.

(1) _{x 2}
14 S + 16 C = 136 
14 S = 136 - 16 C ---- (3)

(2) _{x 7}
14 S + 28 C = 196 
14 S = 196 - 28 C ---- (4)

(3) = (4)
136 - 16 C = 196 - 28 C 
28 C - 16 C = 196 - 136 
12 C = 60

1 C = 60 ÷ 12 = 5 

Cost of 1 cookie = $5 

Number of cookies that David can buy at most
= 61 ÷ 5
= 12 r 1

Most number of cookies that David can buy = 12

Answer(s): 12