Question

At the movies, a couple bought 2 medium drinks and a large popcorn for $13.85. At the same theater, a family bought 3 medium drinks and 2 large popcorns for a total of $23.90. What is the cost of a medium drink? What is the cost of a large popcorn?

Answer 1

Medium drink = $3.8

Large popcorn = $6.25

Explanation:

Assuming the cost of a medium drink to be m and the cost of a large popcorn to be p, we can write these two equations:

`2d+p=13.85` --- (1)

`3d+2p=23.90` --- (2)

Finding the cost of a medium drink and a large popcorn.

From equation (1),
`p=13.85-2d`.

Substituting this value of
`p` in equation (2):

`3d+2p=23.90`

`3d+2(13.85-2d)=23.90`

`3d+27.7-4d=23.90`

`3d-4d=23.90-27.7`

`d=3.8`

Now substituting this value of
`d` to find
`p`:

`p=13.85-2d`

`p=13.85-2(3.8)`

p=
`6.25`

Therefore, the cost of a medium drink is $3.8 while a large popcorn costs $6.25.

Answer 2

a) the cost of one medium drink be $3.80

b) the cost of a large popcorn be $6.25

Explanation:

Let the cost of one medium drink be $x

and the cost of a large popcorn be $y

According to question,

A couple bought 2 medium drinks and a large popcorn for $13.85.

2x + y = 13.85 ..............(1)

A family bought 3 medium drinks and 2 large popcorn for a total of $23.90

3x + 2y = 23.90 ..............(2)

Using Elimination method to solve the system of equation,

Multiply equation (1) by 2 , we get,

4x + 2y = 27.70 ..............(3)

Now, subtract equation (2) from (3), we get,

4x + 2y-(3x + 2y) = 27.70 - 23.90

4x + 2y-3x - 2y = 3.80

4x -3x = 3.80

x = 3.80

Substitute, x = 3.8 in (1) ,

2(3.80) + y = 13.85

7.60 +y = 13.85

y = 6.25

Therefore, the cost of one medium drink be $3.80

and the cost of a large popcorn be $6.25