Daniel had a sum of money. If he bought 8 muffins and 6 cookies, he would be short of $9. If he bought 5 muffins and 4 cookies, he would have $17 left. Given that he had $63, how many cookies could he buy at most?
Cost of 1 muffin = 1 M
Cost of 1 cookie = 1 C

8 M + 6 C - 9 = 63
8 M + 6 C = 63 + 9 
8 M + 6 C = 72 --- (1)

5 M + 4 C + 17 = 63 
5 M + 4 C = 63 - 17 
5 M + 4 C = 46 --- (2)

Make M the same.

(1) _{x 5}
40 M + 30 C = 360 
40 M = 360 - 30 C ---- (3)

(2) _{x 8}
40 M + 32 C = 368 
40 M = 368 - 32 C ---- (4)

(3) = (4)
360 - 30 C = 368 - 32 C 
32 C - 30 C = 368 - 360 
2 C = 8

1 C = 8 ÷ 2 = 4 

Cost of 1 cookie = $4 

Number of cookies that Daniel can buy at most
= 63 ÷ 4
= 15 r 3

Most number of cookies that Daniel can buy = 15

Answer(s): 15