SOLUTION: A woman bought 100 Christmas cards. For the ones that sing a song when you open them, she paid 30 cents each. For the rest she paid 5 cents each. If the cards cost $10.25 in all, h

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A woman bought 100 Christmas cards. For the ones that sing a song when you open them, she paid 30 cents each. For the rest she paid 5 cents each. If the cards cost $10.25 in all, h      Log On


   

Question 1028923: A woman bought 100 Christmas cards. For the ones that sing a song when you open them, she paid 30 cents each. For the rest she paid 5 cents each. If the cards cost $10.25 in all, how many of the expensive kind did she buy?
Found 2 solutions by Edwin McCravy, stanbon:
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of sing-a-songs be x
Let the number of ordinarys be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
card       cards       card      cards
-------------------------------------------
sing-a-songs  x      $0.30       $0.30x
ordinarys     y      $0.05       $0.05y
-------------------------------------------
TOTALS       100      -----      $10.25

 The first equation comes from the second column.

  %28matrix%283%2C1%2CNumber%2Cof%2Csing-a-songs%29%29%22%22%2B%22%22%28matrix%283%2C1%2CNumber%2Cof%2Cordinarys%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Ccards%29%29

                 x + y = 100

 The second equation comes from the last column.
  %28matrix%284%2C1%2CValue%2Cof%2CALL%2Csing-a-songs%29%29%22%22%2B%22%22%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cordinarys%29%29%22%22=%22%22%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccards%29%29

           0.3x + 0.05y = 10.25

Get rid of decimals by multiplying every term by 100:

          30x + 5y = 1025

 So we have the system of equations:
           system%28x+%2B+y+=+100%2C30x+%2B+5y+=+1025%29.

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

           x + y = 100
               y = 100 - x

Substitute (100 - x) for y in 30x + 5y = 1025

  30x + 5(100 - x) = 1025
    30x + 500 - 5x = 1025
          25x + 500 = 1025
               25x = 525
                x = 21 = the number of sing-a-song cards.

Substitute in y = 100 - x
              y = 100 - (21)
              y = 79 ordinarys.

Checking:  21 sing-a-songs is $6.30 and 79 ordinarys is $3.95
            That's 100 cards.
            And indeed $6.30 + $3.95 = $10.25
Edwin

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A woman bought 100 Christmas cards. For the ones that sing a song when you open them, she paid 30 cents each. For the rest she paid 5 cents each. If the cards cost $10.25 in all, how many of the expensive kind did she buy?
---------------
Equations:
s + r = 100 cards
30s + 5r = 1025 cents
-----------------------------
Modify for elimination::
s + r = 100
6s + r = 205
-------------------
Subtract and solve for "s"
5s = 105
s = 21 (# of song cards)
r = 100 -21 = 79 (# of other cards)
----------------------------------
Cheers,
Stan H.