SOLUTION: ann purchased 40 stamps, a mixture of 44 cent stamps and 20 cent stamps. Find the number of each type of stamp if she spent $13.28. Using a system of equations to solve.

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Question 1007859: ann purchased 40 stamps, a mixture of 44 cent stamps and 20 cent stamps. Find the number of each type of stamp if she spent $13.28. Using a system of equations to solve.
Found 2 solutions by tiffany222, Edwin McCravy:
Answer by tiffany222(56) About Me  (Show Source):
You can put this solution on YOUR website!
Let 44 cent stamps be x
Let 20 cent stamps be y
x + y = 40
.44x + .20y = 13.28
Multiply second equation by 5 to eliminate y:
x + y = 40
2.2x + y = 66.4
Subtract:
-1.2x = -26.4
x = 22
Substitute x into original equation to get y:
x + y = 40
22 + y = 40
y = 18
Final Answer:
44 cent stamps = 22
20 cent stamps = 18

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of 44¢ stamps be x
Let the number of 20¢ stamps be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
stamp      stamps     stamp     stamps
-------------------------------------------
44¢s         x        $0.44     $0.44x
20¢s         y        $0.20     $0.20y
-------------------------------------------
TOTALS      40       -----     $13.28

 The first equation comes from the second column.

  %28matrix%283%2C1%2CNumber%2Cof%2C%2244c%27s%22%29%29%22%22%2B%22%22%28matrix%283%2C1%2CNumber%2Cof%2C%2220c%27s%22%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Cstamps%29%29

                 x + y = 40

 The second equation comes from the last column.
  %28matrix%284%2C1%2CValue%2Cof%2CALL%2C%2244c%27s%22%29%29%22%22%2B%22%22%28matrix%284%2C1%2CValue%2Cof%2CALL%2C%2220c%27s%22%29%29%22%22=%22%22%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Cstamps%29%29

           0.44x + 0.20y = 13.28

Get rid of decimals by multiplying every term by 100:

          44x + 20y = 1328

 So we have the system of equations:
           system%28x+%2B+y+=+40%2C44x+%2B+20y+=+1328%29.

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

           x + y = 40
               y = 40 - x

Substitute (40 - x) for y in 44x + 20y = 1328

   44x + 20(40 - x) = 1328
    44x + 800 - 20x = 1328
          24x + 800 = 1328
                24x = 528
                  x = 22 = the number of 44¢s.

Substitute in y = 40 - x
              y = 40 - (22)
              y = 18 = the number of 20¢s.



Checking:  22 44¢s is $9.68 and 18 20¢s is $3.60
            That's 40 stamps.
            And indeed $9.68 + $3.60 = $13.28
Edwin