Question 933954
josh has 25 coins. these are nickels and dimes. if he has 1.95 dollars, how many of each will he have
<pre>
Let the number of nickels be x
Then the number of dimes, using 
ONE PART = TOTAL MINUS OTHER PART,
is 25-x.  
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
NICKELS      x        $0.05    $0.05x 
DIMES      25-x       $0.10    $0.10(25-x)
-------------------------------------------
TOTALS      25        -----    $1.95

 The equation comes from the column on the right

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

0.05x + 0.10(25-x) = 1.95

Get rid of decimals by multiplying every term by 100

     5x + 10(25-x) = 195

    5x + 250 - 10x = 195

         -5x + 250 = 195

               -5x = -55

                 x = 11 = the number of nickels

The number of dimes is 25-x or 25-11 or 14 dimes.

Checking:  11 nickels is $0.55 and 14 dimes is $1.40

And indeed $0.55+$1.40 = $1.95.

Edwin</pre>