Question

At a movie theater, 2 medium drinks and a large popcorn costs $13.85. At the same theater, a family bought 3 medium drinks and 2 large popcorns for a total of $23.90. Which system of equations could be used to find x, the cost of a medium drink and y, the cost of a large popcorn?

A) 2x + y = 13.85
3x + 2y = 23.9
B) 3x + 2y = 13.85
2x + y = 23.9

C) x + 2y = 13.85
3x + 2y = 23.9

D) 2x + y = 13.85
2x + 3y = 23.9

Answer 1

A

Explanation:

The answer is (A) because, first off you have 2 medium drinks. So that is 2x. Second you only have 1 large popcorn. So that is just y. Right now the equation is 2x + y =$13.85. The next part of the problem is the same thing. You have only 1 more medium drink this time, so it is 3x. Then you have 1 more large popcorn, so that is 2y. The final part of the equation is 3x + 2y =$23.90. Since 23.90 is just a decimal you can just get rid of the 0. Now the equation should look like this, 2x + y=$13.85

3x + 2y=$23.9

Answer 2

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.