Answer:
The required system of equations is:
5 m+ 7 n = 113.75
6 m + 14 n = 185.50
The price of 1 bag of popcorn = $10.5
The price of 1 drink = $8.75
Step-by-step explanation:
Let us assume the cost of 1 bag of popcorn = $ m
And, the cost of 1 drink = $ n
Now, Leah spends a total of 113.75 on 5 bags of popcorn and 7 drinks.
Cost of 5 bags + 7 drinks = 5 m + 7 n = $ 113.75
⇒ 5 m+ 7 n = 113.75 .. (1)
Also, Ashley spends a total of 185.50 on 6 bags of popcorn and 14 drinks
Cost of 6 bags + 14 drinks = 6 m + 14 n = $185.50
⇒ 6 m + 14 n = 185.50 .. (2)
So, here the system of equations that can be used to find the price of one bag of popcorn (m) and the price of one drink
(n) are
5 m+ 7 n = 113.75 .. (1)
6 m + 14 n = 185.50 .. (2)
Now, to solve this, Multiply (1) with -2 and add with 2, we get:
-10m + 6m - 14 n + 14 n = 185.5 - 227.5
or, - 4 m = -42 , or m = 42/4 = 10.5
Putting the value of m = 10.5 in 5 m+ 7 n = 113.75 , we get n = 8.75
Hence, the price of 1 bag of popcorn = m = $10.5
And the price of 1 drink = n = $8.75
