SOLUTION: Ron has 15 coins with a total value of $2.55. The coins are nickels and quarters. How many of each does he have ?

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Question 969129: Ron has 15 coins with a total value of $2.55. The coins are nickels and quarters. How many of each does he have ?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
first kind of coin (in quotes)? nickel
value of first kind of coin? .05
second kind of coin in quotes)? quarter
value of second kind of coin? .25
number of coins? 15
total value of coins? 2.55
Let the number of nickels be x
Then the number of quarters, using
ONE PART = TOTAL MINUS OTHER PART,
is 15-x.
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickels      x        $0.05    $0.05x
quarters   15-x       $0.25    $0.25(15-x)
-------------------------------------------
TOTALS      15        -----    $2.55

 The equation comes from the column on the right

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

     0.05x + 0.25(15-x) = 2.55

Get rid of decimals by multiplying every term by 100:

          5x + 25(15-x) = 255

         5x + 375 - 25x = 255

             -20x + 375 = 255

                   -20x = -120

                      x = 6 = the number of nickels.

The number of quarters is 15-x or 15-6 or 9 quarters.

Checking:  6 nickels is $0.30 and 9 quarters is $2.25

            And indeed $0.30 + $2.25 = $2.55
Edwin