Question 1024814
<pre>
Let the number of quarters be x
Let the number of dimes be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
quarters     x      $0.25       $0.25x
dimes        y      $0.10       $0.10y
-------------------------------------------
TOTALS      70      -----      $13.30

 The first equation comes from the second column.

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

                     x + y = 70

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

             0.25x + 0.10y = 13.30

Get rid of decimals by multiplying every term by 100:

                 25x + 10y = 1330

 So we have the system of equations:
           {{{system(x + y = 70,25x + 10y = 1330)}}}.

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

                     x + y = 70
                         y = 70 - x

Substitute (70 - x) for y in 25x + 10y = 1330

          25x + 10(70 - x) = 1330
           25x + 700 - 10x = 1330
                 15x + 700 = 1330
                       15x = 630
                         x = 42 = the number of quarters.

Substitute in y = 70 - x
              y = 70 - (42)
              y = 28 dimes.


Checking:  42 quarters is $10.50 and 28 dimes is $2.80
            That's 70 coins.
            And indeed $10.50 + $2.80 = $13.30
Edwin</pre>