Answer:
The cost of 1 small bag of popcorn = $2.95
The cost of 1 large bag of popcorn = $4.75
Step-by-step explanation:
Here, let us assume the cost of 1 small bag of popcorn = $ m
And, the cost of 1 large bag of popcorn = $ n
So, the cost of 9 small bag = 9 x ( cost of 1 small bag) = 9 x (m) = 9 m
and the cost of 2 large bag = 2 x ( cost of 1 large bag) = 2 x (n) = 2 n
Also, cost of 9 small + 2 large bag of popcorn sold by Ethan for $ 36.05 .
⇒ Total cost of 9 small + 2 large bag of popcorn = 9 m + 2 n
⇒ 9 m + 2 n = $ 36.05 .......... (1)
Also, the cost of 5 small bag = 5 x ( cost of 1 small bag) = 5 m
and the cost of 7 large bag = 7 x ( cost of 1 large bag) = 7 n
Also, cost of 5 small + 7 large bag of popcorn sold by Jack for $ 48 .
⇒ Total cost of 5 small + 7 large bag of popcorn = 5 m + 7 n
⇒ 5 m + 7 n = $ 48 .......... (2)
Now, solving (1) and (2) for the values of m and n , we get
9 m + 2 n = 36.05
5 m + 7 n = 48
Multiply (1) with (-7) and (2) by 2 , add both equation we get:
-63 m - 14 n + 10 m + 14 n = -252.35 + 96
or, - 53 m = -156.35
or, m = 2.95
Now, put the value of m in (1), we get: 5 ( 2.95) + 7 n = 48
or, n = 33.25 /7 = 4.75
Hence the cost of 1 small bag of popcorn = $2.95
The cost of 1 large bag = $4.75
