Question

Angel and Alexander go to the movie theater and purchase refreshments for their friends.


Angel spends a total of $32.50 on 3 drinks and 2 bags of popcorn.


Alexander spends a total of $72.50 on 6 drinks and 10 bags of popcorn.


Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn.


Using these equations, determine and state the price of a drink, to the nearest cent.

Answer 1

Answer:

The price of a drink is $10.

Step-by-step explanation:

Given:

A total of $32.50 is spend by Angel on 3 drinks and 2 bags of popcorn.

A total of $72.50 is spend by Alexander on 6 drinks and 10 bags of popcorn.

Now, to find the price of a drink.

Let the price of one drink be $x.$

And let the price of one bag of popcorn be $y.$

So, total money Angel spends:

$3x+2y=32.50$   .......(1)

Now, total money Alexander spends:

$6x+10y=72.50$  .......(2)

Now, to solve system of equations by multiplying the equation (1) by 2 and then subtracting equation (1) from equation (2):

$3x+2y=32.50\times 2$

$6x+4y=65$  

Now, subtracting:

$6x+10y-(6x+4y)=72.50-65$

$6x+10y-6x-4y=72.50-65$

$6y=7.5$

Dividing both sides by 6 we get:

$y=\ 1.25.$

The price of one bag of popcorn = $1.25.

Now, substituting the value of $y$ in equation (1):

$3x+2y=32.50\\\\3x+2(1.25)=32.50\\\\3x+2.5=32.50$

Subtracting both sides  by 2.5 we get:

$3x=30$

Dividing both sides by 3 we get:

$x=10$ .

The price of a drink = $10.

Therefore, the price of a drink is $10.