Serenity and taylor go to the movie theater and purchase refreshments for their friends. serenity spends a total of $86.50 on 9 drinks and 2 bags of popcorn. taylor spends a total of $89.25 on 3 drinks and 9 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.

Hello there!

If D is the price of one drink and P the price of one bag of popcorn, we know that:

9*D + 2*P = $86.50

3*D + 9*P = $89.25

Now we can isolate one of the therms in the first equation and replace it in the second one:

Lets isolate D in the first equation

9*D + 2*P = $86.50

9*D =   $86.50 - 2*P

D = ( $86.50 - 2*P)/9

now we can replace in in the second equation and obtain the value of P

3*D + 9*P = $89.25

3*( $86.50 - 2*P)/9 + 9*P = $89.25

( $86.50 - 2*P)/3 + 9*P = $89.25

$28.83 - (2/3)P + 9P = $89.25

(9 - 2/3)P = $89.25 - $28.83  = $60.42

(25/3)P = $60.42

P = $60.42*(3/25)= $7.25

So each bag of popcorn cost $7.25.

Now we can replace it in the first equation and find the price for the drinks:

9*D + 2*P = $86.50

9*D + 2*$7.25 = $86.50

9*D + $14.50 = $86.50

9*D = $86.50 - $14.50 = $72

D = $72/9 = $8

So each drink cost $8.

And now we know the price for one bag of popcorn and for one drink,

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