Answer:
3 m + 4 n = $24.25
9 m + n = $37.00 are the required set of equations.
The cost of 1 cold drink = $3.75
The cost of 1 pop corn bag = $3.25
Step-by-step explanation:
Let us assume the cost of 1 drink = $ m
And 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 = $ 24.25
or, 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 = $37.00
or, 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 m
Substitute the value of n in the equation (1),we get:
3 m + 4 n = $24.25 ⇒ 3 m + 4 ( 37 - 9 m ) = 24.25
or, 3 m + 148 - 36 m = 24.25
or, -33 m = -123.75
or, m = 123.75/33 = 3.75, or m = 3.75
Now, n = 37 - 9 m = 37 - 9(3.75) = 3.25, or n = 3.25
Hence the cost of 1 cold drink = m = $3.75
And the cost of 1 pop corn bag = n = $3.25
