Brandon had a sum of money. If he bought 8 macarons and 7 cookies, he would be short of $9. If he bought 3 macarons and 4 cookies, he would have $31 left. Given that he had $66, how many cookies could he buy at most?
Cost of 1 macaron = 1 M
Cost of 1 cookie = 1 C

8 M + 7 C - 9 = 66
8 M + 7 C = 66 + 9 
8 M + 7 C = 75 --- (1)

3 M + 4 C + 31 = 66 
3 M + 4 C = 66 - 31 
3 M + 4 C = 35 --- (2)

Make M the same.

(1) _{x 3}
24 M + 21 C = 225 
24 M = 225 - 21 C ---- (3)

(2) _{x 8}
24 M + 32 C = 280 
24 M = 280 - 32 C ---- (4)

(3) = (4)
225 - 21 C = 280 - 32 C 
32 C - 21 C = 280 - 225 
11 C = 55

1 C = 55 ÷ 11 = 5 

Cost of 1 cookie = $5 

Number of cookies that Brandon can buy at most
= 66 ÷ 5
= 13 r 1

Most number of cookies that Brandon can buy = 13

Answer(s): 13