SOLUTION: Kevin and randy muise have a jar containing 55 coins, all of which are either quarters or nickles. The total value of the coins in the jar is $10.15. How many of each type of coin

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Question 974381: Kevin and randy muise have a jar containing 55 coins, all of which are either quarters or nickles. The total value of the coins in the jar is $10.15. How many of each type of coin do they have?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Let the number of quarters be x
Then the number of nickels, using
ONE PART = TOTAL MINUS OTHER PART,
is 55-x.
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
quarters      x        $0.25    $0.25x
nickels     55-x       $0.05    $0.05(55-x)
-------------------------------------------
TOTALS      55      -----      $10.15

 The equation comes from the column on the right

  %28matrix%284%2C1%2CValue%2Cof%2CALL%2Cquarters%29%29%22%2B%22%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cnickels%29%29%22=%22%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccoins%29%29

0.25x + 0.05(55-x) = 10.15

Get rid of decimals by multiplying every term by 100:

     25x + 5(55-x) = 1015

    25x + 275 - 5x = 1015

        20x + 275 = 1015

              20x = 740

                 x = 37 = the number of quarters.

The number of nickels is 55-x or 55-37 or 18 nickels.

Checking:  37 quarters is $9.25 and 18 nickels is $0.90
            That's 55 coins.
            And indeed $9.25 + $0.90 = $10.15
Edwin