Answer: 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,
