Question 1020549
<pre>
Let the number of nickels be x
Let the number of dimes be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickels       x      $0.05       $0.05x
dimes         y      $0.10       $0.10y
-------------------------------------------
TOTALS       12      -----       $1.00

 The first equation comes from the second column.

  {{{(matrix(3,1,Number,of,nickels))}}}{{{""+""}}}{{{(matrix(3,1,Number,of,dimes))}}}{{{""=""}}}{{{(matrix(4,1,total,number,of,coins))}}}
                 x + y = 12

 The second equation comes from the last column.
  {{{(matrix(4,1,Value,of,ALL,nickels))}}}{{{""+""}}}{{{(matrix(4,1,Value,of,ALL,dimes))}}}{{{""=""}}}{{{(matrix(5,1,Total,value,of,ALL,coins))}}}

           0.05x + 0.10y = 1

Get rid of decimals by multiplying every term by 100:

                5x + 10y = 100

 So we have the system of equations:
           {{{system(x + y = 12,5x + 10y = 100)}}}.

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

                   x + y = 12
                       y = 12 - x

Substitute (12 - x) for y in 5x + 10y = 100

         5x + 10(12 - x) = 100
          5x + 120 - 10x = 100
               -5x + 120 = 100
                     -5x = -20
                       x = 4 = the number of nickels.

Substitute in y = 12 - x
              y = 12 - (4)
              y = 8 dimes.


Checking:  4 nickels is $0.20 and 8 dimes is $0.80
            That's 12 coins.
            And indeed $0.20 + $0.80 = $1.00
Edwin</pre>