SOLUTION: Madison and Gabriella go to the movie theater and purchase refreshments for theirs. Madison spends a total of $136.50 on 6 drinks and 14 bags of popcorn. Gabriella spends a total o

Question 1013341: Madison and Gabriella go to the movie theater and purchase refreshments for theirs. Madison spends a total of $136.50 on 6 drinks and 14 bags of popcorn. Gabriella spends a total of $41.00 on 7 drinks and 2 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. Determine and state the price of a drink and a popcorn to the nearest cent.
Found 2 solutions by Boreal, stanbon:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
6D+14P=136.50; drinks are D, popcorn is P
7D+2P=41
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6D+14P=136.50
-49D-14P=-287,multiplying the second by -7
-43D=-150.50, add the two together.
Drinks are $3.50
substitute into second equation
$24.50+2P=41
2P=16.50
P=8.25
=============
Check with first equation
21+115.50=136.50
Drinks are $3.50
Popcorn is $8.50
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Madison spends a total of $136.50 on 6 drinks and 14 bags of popcorn. Gabriella spends a total of $41.00 on 7 drinks and 2 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.
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Equations:
6d + 14b = 136.50
7d + 2b = 41
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Modify for elimination:
6d + 14b = 136.50
49d + 14b = 7*41
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Subtract and solve for "d":
43d = 150.5
d = $3.50 (cost of one drink)
-----------------
Solve for "b:
7d + 2b = 41
----
24.50 + 2b = 41
2b = 16.50
b = $8.25 (cost of one bag)
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Cheers,
Stan H.
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