SOLUTION: jack bought 34 stamps at the post office. some were 37cents and the rest were 80cents. if the total cost of the stamps was $16.45, how many of each type did he buy?

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Question 999707: jack bought 34 stamps at the post office. some were 37cents and the rest were 80cents. if the total cost of the stamps was $16.45, how many of each type did he buy?
Found 2 solutions by josgarithmetic, AnlytcPhil:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, count of the 37 cent stamps
y, count of the 80 cent stampts
system%28x%2By=34%2C37x%2B80y=16.45%29

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of 37c stamps be x
Let the number of 80c stamps be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
stamp      stamps     stamp     stamps
-------------------------------------------
37c stamps    x       $0.37     $0.37x
80c stamps    y       $0.80     $0.80y
-------------------------------------------
TOTALS       34      -----     $16.45

 The first equation comes from the second column.

  %28matrix%283%2C1%2CNumber%2Cof%2C37c+stamps%29%29%22%22%2B%22%22%28matrix%283%2C1%2CNumber%2Cof%2C80c+stamps%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Cstamps%29%29

                 x + y = 34

  %28matrix%284%2C1%2CValue%2Cof%2CALL%2C37c+stamps%29%29%22%22%2B%22%22%28matrix%284%2C1%2CValue%2Cof%2CALL%2C80c+stamps%29%29%22%22=%22%22%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Cstamps%29%29

           0.37x + 0.8y = 16.45

Get rid of decimals by multiplying every term by 100:

          37x + 80y = 1645

 So we have the system of equations:
           system%28x+%2B+y+=+34%2C37x+%2B+80y+=+1645%29.

We solve by substitution.  Solve the first equation for y:

           x + y = 34
               y = 34 - x

Substitute (34 - x) for y in 37x + 80y = 1645

      37x + 80(34 - x) = 1645
      37x + 2720 - 80x = 1645
           -43x + 2720 = 1645
                  -43x = -1075
                x = 25 = the number of 37c stamps.

Substitute in y = 34 - x
              y = 34 - (25
              y = 9 80c stamps.

The number of 80c stamps is 34-y or 34-9 or 25 80c stamps.

Checking:  25 37c stamps is $9.25 and 9 80c stamps is $7.20
            That's 34 stamps.
            And indeed $9.25 + $7.20 = $16.45

Edwin