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