Brianna and Chloe go to the movie theater and purchase refreshments for their friends.Brianna spends a total of $24.25 on 3 drinks and 4 bags of popcorn.Chloe spends a total of $37.00 on 9 drinks and 1 bag of popcorn.Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn.Using these equations, determine and state the price of a bag of popcorn, to the nearest cent

Answer:3 m + 4  n = $24.25 9 m +   n = $37.00  are the required set of equations.The cost of 1 cold drink  = $3.75The cost of 1 pop corn bag  = $3.25Step-by-step explanation:Let us assume the cost of 1 drink = $ mAnd the cost of 1 bag of popcorn = $ n Now, Brianna buys 3 drinks + 4 bag popcorn  for  $24.25⇒ Cost of 3 drinks +  4 bag popcorn =  $ 24.25or, 3 ( Cost of 1 drink) + 4 ( Cost of i bag popcorn)  = $ 24.25⇒ 3 m + 4  n = $24.25  ...  (1)Also, Chloe buys 9 drinks + 1 bag popcorn  for  $37.00⇒ Cost of 9 drinks +  1 bag popcorn =  $37.00or, 9 ( Cost of 1 drink) + 1 ( Cost of 1 bag popcorn)  = $37.00⇒ 9 m +   n = $37.00 ...  (2)Now, solving equation (1) and (2) ,we get:3 m + 4  n = $24.25 9 m +   n = $37.00   ⇒ n  = 37 -  9 mSubstitute the value of n in the equation (1),we get:3 m + 4  n = $24.25  ⇒ 3  m + 4 ( 37 - 9 m ) = 24.25or, 3 m + 148 - 36 m = 24.25or, -33 m = -123.75or, m = 123.75/33 =  3.75, or m = 3.75Now, n = 37 - 9 m = 37  - 9(3.75)  =  3.25, or n = 3.25Hence the cost of 1 cold drink =  m = $3.75And the cost of 1 pop corn bag  =  n  = $3.25