Jack had a sum of money. If he bought 5 macarons and 6 cookies, he would be short of $19. If he bought 2 macarons and 3 cookies, he would have $8 left. Given that he had $30, how many cookies could he buy at most?
Cost of 1 macaron = 1 M
Cost of 1 cookie = 1 C

5 M + 6 C - 19 = 30
5 M + 6 C = 30 + 19 
5 M + 6 C = 49 --- (1)

2 M + 3 C + 8 = 30 
2 M + 3 C = 30 - 8 
2 M + 3 C = 22 --- (2)

Make M the same.

(1) _{x 2}
10 M + 12 C = 98 
10 M = 98 - 12 C ---- (3)

(2) _{x 5}
10 M + 15 C = 110 
10 M = 110 - 15 C ---- (4)

(3) = (4)
98 - 12 C = 110 - 15 C 
15 C - 12 C = 110 - 98 
3 C = 12

1 C = 12 ÷ 3 = 4 

Cost of 1 cookie = $4 

Number of cookies that Jack can buy at most
= 30 ÷ 4
= 7 r 2

Most number of cookies that Jack can buy = 7

Answer(s): 7