Ethan sold 9 small bags of popcorn and 2 large bags and made $36.05. jack sold 5 small bags and 7 large bags and made $48.00. find the cost of a small bag and large bag of popcorn.

small bag of popcorn costs $2.95 and large bag of popcorn costs $4.75

Step-by-step 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

Thanks

Step-by-step explanation: