Question 1025471
<pre>
Let the number of quarters be x
Let the number of nickels be y

                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
quarters      x       $0.25      $0.25x
nickels       y       $0.05      $0.05y
-------------------------------------------
TOTALS       79      -----       $12.75

 The first equation comes from the second column.

  {{{(matrix(3,1,Number,of,quarters))}}}{{{""+""}}}{{{(matrix(3,1,Number,of,nickels))}}}{{{""=""}}}{{{(matrix(4,1,total,number,of,coins))}}}
                
              x + y = 79

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

      0.25x + 0.05y = 12.75

Get rid of decimals by multiplying every term by 100:

           25x + 5y = 1275

 So we have the system of equations:

           {{{system(x + y = 79,25x + 5y = 1275)}}}.

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

              x + y = 79
                  y = 79 - x
 
Substitute (79 - x) for y in 25x + 5y = 1275

    25x + 5(79 - x) = 1275
     25x + 395 - 5x = 1275
          20x + 395 = 1275
                20x = 880
                  x = 44 = the number of quarters.

Substitute in y = 79 - x
              y = 79 - (44)
              y = 35 nickels.


Checking:  44 quarters is $11.00 and 35 nickels is $1.75
            That's 79 coins.
            And indeed $11.00 + $1.75 = $12.75
Edwin</pre>