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?

a) the cost of one medium drink be $3.80

b) the cost of a large popcorn be $6.25

Step-by-step 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

Medium drink = $3.8

Large popcorn = $6.25

Step-by-step 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:

--- (1)

--- (2)

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

From equation (1), .

Substituting this value of in equation (2):

Now substituting this value of to find :

p=

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