Final answer:
The cost of one large popcorn at the movie theater is $7.55 and one large drink is $5.85. When these are added together, the total cost for one large popcorn and one large drink is $13.40.
Step-by-step explanation:
To determine the cost of one large popcorn and one large drink at the movie theater, we can set up a system of equations based on the information given. The first person purchased 2 large popcorns and 4 large drinks for a total of $38.50, which we can express as 2P + 4D = 38.50. The second person purchased 1 large popcorn and 3 large drinks for a total of $25.10, which is written as P + 3D = 25.10.
To solve this system of equations, we'll use the substitution or elimination method. The elimination method involves lining up both equations so one of the variables can be eliminated:
- (1) 2P + 4D = 38.50
- (2) P + 3D = 25.10
Multiplying the second equation by 2 gives us 2P + 6D = 50.20. Then, subtracting the first equation from this new equation will cancel out the P term:
- (3) 2D = 50.20 - 38.50
- (3) 2D = 11.70
- (3) D = 5.85
So, the cost of a large drink is $5.85. We substitute this value into one of our original equations to find the price of a large popcorn:
- (2) P + 3(5.85) = 25.10
- (2) P + 17.55 = 25.10
- (2) P = 25.10 - 17.55
- (2) P = 7.55
Therefore, the cost of a large popcorn is $7.55. To find the total cost for one of each, you simply add the price of one large drink and one large popcorn: $7.55 + $5.85 = $13.40.