Bobby had a sum of money. If he bought 8 macarons and 6 cookies, he would be short of $4. If he bought 5 macarons and 4 cookies, he would have $18 left. Given that he had $56, how many cookies could he buy at most?
Cost of 1 macaron = 1 M
Cost of 1 cookie = 1 C

8 M + 6 C - 4 = 56
8 M + 6 C = 56 + 4 
8 M + 6 C = 60 --- (1)

5 M + 4 C + 18 = 56 
5 M + 4 C = 56 - 18 
5 M + 4 C = 38 --- (2)

Make M the same.

(1) _{x 5}
40 M + 30 C = 300 
40 M = 300 - 30 C ---- (3)

(2) _{x 8}
40 M + 32 C = 304 
40 M = 304 - 32 C ---- (4)

(3) = (4)
300 - 30 C = 304 - 32 C 
32 C - 30 C = 304 - 300 
2 C = 4

1 C = 4 ÷ 2 = 2 

Cost of 1 cookie = $2 

Number of cookies that Bobby can buy at most
= 56 ÷ 2
= 28 r 0

Most number of cookies that Bobby can buy = 28

Answer(s): 28