SOLUTION: aviva has a total of 56 coins, all which are either dimes or nickels . the total value of the coins is $5.05. find the number of each coin?

Question 922700: aviva has a total of 56 coins, all which are either dimes or nickels . the total value of the coins is $5.05. find the number of each coin?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
Aviva has a total of 56 coins, all which are either dimes or nickels. The total
value of the coins is $5.05. Find the number of each coin?

Let the number of nickels be x
Then the number of dimes, using 
ONE PART = TOTAL MINUS OTHER PART,
is 56-x.  
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
NICKELS      x        $0.05    $0.05x 
DIMES      56-x       $0.10    $0.10(56-x)
-------------------------------------------
TOTALS      56        -----    $5.05

 The equation comes from the column on the right

  

0.05x + 0.10(56-x) = 5.05

Get rid of decimals by multiplying every term by 100

     5x + 10(56-x) = 505

    5x + 560 - 10x = 505

         -5x + 560 = 505

               -5x = -55

                 x = 11 = the number of nickels

The number of dimes is 56-x or 56-11 or 45 dimes.

Checking:  11 nickels is $0.55 and 45 dimes is $4.50

And indeed $0.55+4.50 = $5.05.

Edwin

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