Answer:
small bag of popcorn costs $2.95 and large bag of popcorn costs $4.75
Explanation:
Let x = cost of a small bag of popcorn
Let y = cost of a large bag of popcorn
Ethan sold 9 small bags of popcorn and 2 large bags and made $36.05. This means
9x+2y = 36.05 - - - - - -- - 1
Jack sold 5 small bags and 7 large bags and made $48.00.
This means
5x + 7y = 48.00 - - - - - - - 2
Using method of elimination,
Multiply equation 1 by 5 and equation 2 by 9. It becomes
45x + 10y = 180.25
45x + 63y = 432
Subtracting,
-53y = -251.75
y = -251.75/-53
y= 4.75
Substitute y = 4.75 into equation 1. It becomes
9x + 2(4.75) = 36.05
9x = 36.05- 9.5= 26.55
x = 26.55/9
x = 2.95