Question 992200
<pre>
You can either do it with 1 unknown or with 2 unknowns.
I'll do it both ways.

With 1 unknown

Let the number of nickels be x
Then the number of quarters, using
ONE PART = TOTAL MINUS OTHER PART,
is 11-x.
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickels      x        $0.05    $0.05x
quarters   11-x       $0.25    $0.25(11-x)
-------------------------------------------
TOTALS      11        -----    $1.55

 The equation comes from the column on the right

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

        0.05x + 0.25(11-x) = 1.55

Get rid of decimals by multiplying every term by 100:

             5x + 25(11-x) = 155

            5x + 275 - 25x = 155

                -20x + 275 = 155

                      -20x = -120

                         x = 6 = the number of nickels.

The number of quarters is 11-x or 11-6 or 5 quarters.

Checking:  6 nickels is $0.30 and 5 quarters is $1.25
            That's 11 coins.
            And indeed $0.30 + $1.25 = $1.55


---------------------
With two unknowns

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       11      -----     $1.55

 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 = 11

 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 = 1.55

Get rid of decimals by multiplying every term by 100:

                5x + 25y = 155

 So we have the system of equations:

           {{{system(x + y = 11,5x + 25y = 155)}}}.

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

           x + y = 11
               y = 11 - x

Substitute (11 - x) for y in 5x + 25y = 155

  5x + 25(11 - x) = 155
   5x + 275 - 25x = 155
       -20x + 275 = 155
             -20x = -120
                x = 6 = the number of nickels.

Substitute in y = 11 - x
              y = 11 - (6
              y = 5 quarters.

The number of quarters is 11-x or 11-6 or 5 quarters.

Checking:  6 nickels is $0.30 and 5 quarters is $1.25
            That's 11 coins.
            And indeed $0.30 + $1.25 = $1.55dwin</pre>

Edwin</pre>