The correct system of equations that could be used to find x, the cost of a medium drink, and y, the cost of a large popcorn, is:
A) 2x + y = 13.85 3x + 2y = 23.9
To arrive at these equations, you can use the information given in the question to set up a system of linear equations. You know that 2 medium drinks and a large popcorn cost $13.85, so you can write:
2x + y = 13.85
where x is the cost of a medium drink and y is the cost of a large popcorn.
You also know that 3 medium drinks and 2 large popcorns cost $23.90, so you can write:
3x + 2y = 23.9
Then , you can solve the system of equations for x and y using any method you prefer, such as elimination or substitution. For example, one way to solve the system is to multiply the first equation by 3 to eliminate y:
6x + 3y = 41.55
Then you can subtract the second equation from this equation:
6x + 3y - (3x + 2y) = 41.55 - 23.9
Simplifying this equation gives:
3x + y = 17.65
You now have two equations to solve for x and y:
3x + y = 17.65 3x + 2y = 23.9
This system of equations is equivalent to the system shown in answer A.