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

Answer:

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

Answer 2

Answer:

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:

$2d+p=13.85$ --- (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.