SOLUTION: A bank has only dimes and quarters worth $15.40. There are 100 coins in the bank. How many are dimes?

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Question 925675: A bank has only dimes and quarters worth $15.40. There are 100 coins in the bank. How many are dimes?
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
Aviva has a total of 100 coins, all which are either dimes or QUARTERs. The total
value of the coins is $5.05. Find the number of each coin?
Let the number of QUARTERs be x
Then the number of dimes, using
ONE PART = TOTAL MINUS OTHER PART,
is 100-x.
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
QUARTERS      x       $0.25    $0.25x
DIMES     100-x       $0.10    $0.10(100-x)
-------------------------------------------
TOTALS      100        -----   $15.40

 The equation comes from the column on the right

  %28matrix%284%2C1%2CValue%2Cof%2CALL%2CQUARTERs%29%29%22%22%2B%22%22%28matrix%284%2C1%2CValue%2Cof%2CALL%2CDIMES%29%29%22%22=%22%22%28matrix%284%2C1%2CTotal%2Cvalue%2Cof%2CCOINS%29%29

0.25x + 0.10(100-x) = 15.40

Get rid of decimals by multiplying every term by 100

     25x + 10(100-x) = 1540

    25x + 1000 - 10x = 1540

          15x + 1000 = 1540

                 15x = 540

                   x = 36 = the number of QUARTERs

The number of dimes is 100-x or 100-36 or 64 dimes.

Checking:  36 QUARTERs is $9.00 and 64 dimes is $6.40

And indeed $9.00+$6.40 = $15.40.

Edwin