Question 985545
<pre>
Let the number of Nickels be x
Let the number of Quarters be y

                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
Nickels       x      $0.05     $0.05x
Quarters      y      $0.25     $0.25y
-------------------------------------------
TOTALS       25      -----     $3.85

 The first equation comes from the second column.

  {{{(matrix(3,1,Number,of,Nickels))}}}{{{""+""}}}{{{(matrix(3,1,Number,of,Quarters))}}}{{{""=""}}}{{{(matrix(4,1,total,number,of,coins))}}}

             x + y = 25

The second equation comes from the last column:

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

     0.05x + 0.25y = 3.85

Get rid of decimals by multiplying every term by 100:

          5x + 25y = 385

 So we have the system of equations:

          {{{system(x + y = 25,5x + 25y = 385)}}}.

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

             x + y = 25
                 y = 25 - x

Substitute (25 - x) for y in 5x + 25y = 385

   5x + 25(25 - x) = 385
    5x + 625 - 25x = 385
        -20x + 625 = 385
              -20x = -240
                 x = 12 = the number of Nickels.

Substitute in y = 25 - x
              y = 25 - (12)
              y = 13 Quarters.

The number of Quarters is 25-x or 25-12 or 13 Quarters.

Checking:  12 Nickels is $0.60 and 13 Quarters is $3.25
            That's 25 coins.
            And indeed $0.60 + $3.20 = $3.85

Edwin</pre>