SOLUTION: You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda cost $0.50. At the end of the game you made a total of $78.50.You sold a total of 87 hot dogs and sodas c

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda cost $0.50. At the end of the game you made a total of $78.50.You sold a total of 87 hot dogs and sodas c      Log On

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Question 969119: You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda cost $0.50. At the end of the game you made a total of $78.50.You sold a total of 87 hot dogs and sodas combined. How many hot dogs and soda were sold?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of hot dogs be x.
Then the number of sodas, using
ONE PART = TOTAL MINUS OTHER PART,
is 87-x.
                      Money      Money
          Number      from       from
           sold       EACH        ALL
-------------------------------------------
hot dogs     x        $1.50     $1.50x
sodas      87-x       $0.50     $0.50(87-x)
-------------------------------------------
TOTALS      87        -----    $78.50

 The equation comes from the column on the right

%28matrix%284%2C1%2Cmoney%2Cfrom%2CALL%2Chot_dogs%29%29%22%22%2B%22%22%28matrix%284%2C1%2CMoney%2Cfrom%2CALL%2Csodas%29%29%22%22=%22%22%28matrix%284%2C1%2CTotal%2Cmoney%2Ctaken%2Cin%29%29

1.50x + 0.50(87-x) = 78.50

Get rid of decimals by multiplying every term by 100:

   150x + 50(87-x) = 7850

 150x + 4350 - 50x = 7850

       100x + 4350 = 7850

              100x = 3500

                 x = 35 = the number of hot dogs.

The number of sodas is 87-x or 87-35 or 52 sodas.

Checking:  35 hot dogs is $52.50 and 52 sodas is $26.00

            And indeed $52.50 + $26.00 = $78.50

Edwin