Brandon had a sum of money. If he bought 7 cookies and 8 muffins, he would be short of $36. If he bought 2 cookies and 4 muffins, he would have $10 left. Given that he had $38, how many muffins could he buy at most?
Cost of 1 cookie = 1 C
Cost of 1 muffin = 1 M

7 C + 8 M - 36 = 38
7 C + 8 M = 38 + 36 
7 C + 8 M = 74 --- (1)

2 C + 4 M + 10 = 38 
2 C + 4 M = 38 - 10 
2 C + 4 M = 28 --- (2)

Make C the same.

(1) _{x 2}
14 C + 16 M = 148 
14 C = 148 - 16 M ---- (3)

(2) _{x 7}
14 C + 28 M = 196 
14 C = 196 - 28 M ---- (4)

(3) = (4)
148 - 16 M = 196 - 28 M 
28 M - 16 M = 196 - 148 
12 M = 48

1 M = 48 ÷ 12 = 4 

Cost of 1 muffin = $4 

Number of muffins that Brandon can buy at most
= 38 ÷ 4
= 9 r 2

Most number of muffins that Brandon can buy = 9

Answer(s): 9