Question 934184
john has a total of 13 coins in his pocket. of the 13 coins they are all either
quarters or dimes. the total value of the coins is $2.50. how many quarters does
john have in his pocket?

<pre>
Let the number of nickels be x
Then the number of dimes, using 
ONE PART = TOTAL MINUS OTHER PART,
is 13-x.  
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
QUARTERS     x        $0.25    $0.25x 
DIMES      13-x       $0.10    $0.10(13-x)
-------------------------------------------
TOTALS      13        -----    $2.50

 The equation comes from the column on the right

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

0.25x + 0.10(13-x) = 2.50

Get rid of decimals by multiplying every term by 100

     25x + 10(13-x) = 250

    25x + 130 - 10x = 250

          15x + 130 = 250

                15x = 120

                  x = 8 = the number of quarters

The number of dimes is 13-x or 13-8 or 5 dimes.

Checking:  8 quarters is $2.00 and 5 dimes is $0.50

And indeed $2.00+$0.50 = $2.50.

Edwin</pre>