Question 1004829
<pre>
The problem can also be done using only one
unknown or variable:

Let the number of P100s be x
Then the number of P50s, using
ONE PART = TOTAL MINUS OTHER PART,
is 117-x.
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
bill        bills      bill      bills
-------------------------------------------
P100s        x        P100     P100x
P50s       117-x       P50     P50(117-x)
-------------------------------------------
TOTALS      117      -----     P9950

 The equation comes from the column on the right

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

           100x + 50(117-x) = 9950

           100x + 50(117-x) = 9950

          100x + 5850 - 50x = 9950

                 50x + 5850 = 9950

                        50x = 4100

                     x = 82 = the number of P100s.

The number of P50s is 117-x or 117-82 or 35 P50s.

Checking:  82 P100s is P8200 and 35 P50s is P1750

            That's 117 coins.

            And indeed P8200 + P1750 = P9950
Edwin</pre>