Question 1028923
<pre>
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.

  {{{(matrix(3,1,Number,of,sing-a-songs))}}}{{{""+""}}}{{{(matrix(3,1,Number,of,ordinarys))}}}{{{""=""}}}{{{(matrix(4,1,total,number,of,cards))}}}

                 x + y = 100

 The second equation comes from the last column.
  {{{(matrix(4,1,Value,of,ALL,sing-a-songs))}}}{{{""+""}}}{{{(matrix(4,1,Value,of,ALL,ordinarys))}}}{{{""=""}}}{{{(matrix(5,1,Total,value,of,ALL,cards))}}}

           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(x + y = 100,30x + 5y = 1025)}}}.

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</pre>