Julian had a sum of money. If he bought 8 macarons and 7 cookies, he would be short of $25. If he bought 3 macarons and 4 cookies, he would have $11 left. Given that he had $37, how many cookies could he buy at most?
Cost of 1 macaron = 1 M
Cost of 1 cookie = 1 C

8 M + 7 C - 25 = 37
8 M + 7 C = 37 + 25 
8 M + 7 C = 62 --- (1)

3 M + 4 C + 11 = 37 
3 M + 4 C = 37 - 11 
3 M + 4 C = 26 --- (2)

Make M the same.

(1) _{x 3}
24 M + 21 C = 186 
24 M = 186 - 21 C ---- (3)

(2) _{x 8}
24 M + 32 C = 208 
24 M = 208 - 32 C ---- (4)

(3) = (4)
186 - 21 C = 208 - 32 C 
32 C - 21 C = 208 - 186 
11 C = 22

1 C = 22 ÷ 11 = 2 

Cost of 1 cookie = $2 

Number of cookies that Julian can buy at most
= 37 ÷ 2
= 18 r 1

Most number of cookies that Julian can buy = 18

Answer(s): 18