Question 925819
Anna has 19 coins, all nickels and dimes. the coins' total 
value is $1.55. How many nickels and dimes does she have?
<pre>
Let the number of nickels be x
Then the number of dimes, using 
ONE PART = TOTAL MINUS OTHER PART,
is 19-x.  
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
NICKELS      x        $0.05    $0.05x 
DIMES      19-x       $0.10    $0.10(19-x)
-------------------------------------------
TOTALS      19        -----    $1.55

 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(19-x) = 1.55

Get rid of decimals by multiplying every term by 100

     5x + 10(19-x) = 155

    5x + 190 - 10x = 155

         -5x + 190 = 155

               -5x = -35

                 x = 7 = the number of nickels

The number of dimes is 19-x or 19-7 or 12 dimes.

Checking:  7 nickels is $0.35 and 12 dimes is $1.20

That's 7+12=19 coins and indeed $0.35+$1.20 = $1.55.

Edwin</pre>