Question 1037964
<pre><b>
Let the number of dimes be x
Let the number of quarters be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
dimes         x      $0.10       $0.10x
quarters      y      $0.25       $0.25y
-------------------------------------------
TOTALS       37      -----       $5.95

 The first equation comes from the "Number of coins" column.

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

                 x + y = 37

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

         0.10x + 0.25y = 5.95

Get rid of decimals by multiplying every term by 100:

             10x + 25y = 595

 So we have the system of equations:
           {{{system(x + y = 37,10x + 25y = 595)}}}.

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

                 x + y = 37
                     y = 37 - x

Substitute (37 - x) for y in 10x + 25y = 595

      10x + 25(37 - x) = 595
       10x + 925 - 25x = 595
            -15x + 925 = 595
                  -15x = -330
                x = 22 = the number of dimes.

Substitute in y = 37 - x
              y = 37 - (22)
              y = 15 quarters.

Checking:  22 dimes is $2.20 and 15 quarters is $3.75
            That's 37 coins.
            And indeed $2.20 + $3.75 = $5.95
Edwin</pre></b>