Question 1004829
<pre>
Let the number of P100's be x
Let the number of P50's be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
bill        bills      bill      bills
-------------------------------------------
P100s        x        P100      P100x
P50s         y         P50       P50y
-------------------------------------------
TOTALS      117      -----      P9950

 The first equation comes from the second column.

  {{{(matrix(3,1,Number,of,P100s))}}}{{{""+""}}}{{{(matrix(3,1,Number,of,P50s))}}}{{{""=""}}}{{{(matrix(4,1,total,number,of,bills))}}}
                 x + y = 117

 The second equation comes from the last column.

  {{{(matrix(4,1,Value,of,ALL,P100s))}}}{{{""+""}}}{{{(matrix(4,1,Value,of,ALL,P50s))}}}{{{""=""}}}{{{(matrix(5,1,Total,value,of,ALL,bills))}}}

           100x + 50y = 9950

 So we have the system of equations:
           {{{system(x + y = 117,100x + 50y = 9950)}}}.

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

           x + y = 117
               y = 117 - x

Substitute (117 - x) for y in 100x + 50y = 9950

   100x + 50(117 - x) = 9950
    100x + 5850 - 50x = 9950
           50x + 5850 = 9950
                  50x = 4100
                    x = 82 = the number of P100s.

Substitute in y = 117 - x
              y = 117 - (82)
              y = 35 P50s.

Checking:  82 P100s is P8200 and 35 P50s is P1750
            That's 117 bills.
            And indeed P8200 + P1750 = P9950
Edwin</pre>