The price of two bags of popcorn and three drinks is #$18.25#. The price of four bags of popcorn and two drinks is #$27.50#. What is the price of one bag of popcorn and one drink?

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Answer 1 · 2015-06-14T19:22:32

Let #p# be the price of a bag of popcorn and #d# be the price of a drink.

Then #2p+3d = 18.25# and #4p+2d = 27.50#

We can isolate an expression for #d# from the second equation:

First divide both side by #2# to get:

#2p+d = 13.75#

Subtract #2p# from both sides to get:

#d = 13.75 - 2p#

Now substitute this into the first equation as follows:

#18.25 = 2p+3d#

#= 2p+3(13.75-2p)#

#=2p+41.25-6p#

#=41.25-4p#

Add #4p# to both ends to get:

#4p+18.25 = 41.25#

Subtract #18.25# from both sides to get:

#4p = 23.00#

Divide both sides by #4# to get:

#p = 5.75#

Then use this value for #p# to find #d#:

#d = 13.75 - 2p#

#= 13.75 - (2xx5.75)#

#= 13.75 - 11.50#

#= 2.25#

So the price for 1 drink is $2.25, 1 bag of popcorn is $5.75 and both together is $8.