Answer:
The cost of 5 bags of popcorn and 2 sodas is 14.25 units.
Step-by-step explanation:
We are given the following in the question:
Let x units be the cost of a popcorn bag and y units be cost of soda.
The cost of 4 bags of popcorn and 3 sodas is 13.50.
Thus, we can write the equation:
![4x + 3y = 13.50](https://tex.z-dn.net/?f=4x%20%2B%203y%20%3D%2013.50)
The cost of 2 bags of popcorn and 5 sodas is 12.00
Thus, we can write the equation:
![2x+5y=12](https://tex.z-dn.net/?f=2x%2B5y%3D12)
Solving the two equations, we get,
![4x + 3y-(4x+10y) = 13.5 - 24\\\Rightarrow -7y =10.5\\\Rightarrow y = 1.5\\\Rightarrow 2x + 5(1.5) = 12\\\Rightarrow x = 2.25](https://tex.z-dn.net/?f=4x%20%2B%203y-%284x%2B10y%29%20%3D%2013.5%20-%2024%5C%5C%5CRightarrow%20-7y%20%20%3D10.5%5C%5C%5CRightarrow%20y%20%3D%201.5%5C%5C%5CRightarrow%202x%20%2B%205%281.5%29%20%3D%2012%5C%5C%5CRightarrow%20x%20%3D%202.25)
Thus, the cost of popcorn bag is 2.25 units and the cost of a soda is 1.5 units.
Cost of 5 bags and 2 sodas
=![=5x+2y\\=5(2.25) + 2(1.5)\\=14.25](https://tex.z-dn.net/?f=%3D5x%2B2y%5C%5C%3D5%282.25%29%20%2B%202%281.5%29%5C%5C%3D14.25)
Thus, cost of 5 bags of popcorn and 2 sodas is 14.25 units.