Question 927750
Emily has a total of 20 dimes and nickels. The total amount she has is $1.60. How many of each coin does she have?
<pre>
Let the number of nickels be x
Then the number of dimes, using
ONE PART = TOTAL MINUS OTHER PART,
is 20-x.
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
NICKELS      x        $0.05    $0.05x
DIMES      20-x       $0.10    $0.10(20-x)
-------------------------------------------
TOTALS      20        -----    $1.60

 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(20-x) = 1.60

Get rid of decimals by multiplying every term by 100

     5x + 10(20-x) = 160

    5x + 200 - 10x = 160

         -5x + 200 = 160

               -5x = -40

                 x = 8 = the number of nickels

The number of dimes is 20-x or 20-8 or 12 dimes.

Checking:  8 nickels is $0.40 and 12 dimes is $1.20

And indeed $0.40+$1.20 = $1.60.

Edwin</pre>