Question 970231
<pre>
Let the number of nickels be x
Then the number of dimes, using
ONE PART = TOTAL MINUS OTHER PART,
is 50-x.
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickels      x       $0.05    $0.05x
dimes      50-x      $0.10    $0.10(50-x)
-------------------------------------------
TOTALS      50        -----   $4.30

 The equation comes from the column on the right

  {{{(matrix(4,1,Value,of,ALL,nickels))}}}{{{""+""}}}{{{(matrix(4,1,Value,of,ALL,dimes))}}}{{{""=""}}}{{{(matrix(5,1,Total,value,of,ALL,coins))}}}

   0.05x + 0.10(50-x) = 4.30

Get rid of decimals by multiplying every term by 100:

        5x + 10(50-x) = 430

       5x + 500 - 10x = 430

            -5x + 500 = 430

                  -5x = -70

                    x = 14 = the number of nickels.

The number of dimes is 50-x or 50-14 or 36 dimes.

Checking:  14 nickels is $0.70 and 36 dimes is $3.60
            That's 50 coins.
            And indeed $0.70 + $3.60 = $4.30
Edwin</pre>