SOLUTION: Ron has 11 coins with a total value of $1.35. The coins are nickels and quarters. How many of each coin does he have?

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Question 969372: Ron has 11 coins with a total value of $1.35. The coins are nickels and quarters. How many of each coin does he have?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of nickels be x
Then the number of quarters, using
ONE PART = TOTAL MINUS OTHER PART,
is 11-x.
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickels      x        $0.05      $0.05x
quarters   11-x       $0.25      $0.25(11-x)
-------------------------------------------
TOTALS      11        -----      $1.35

 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(11-x) = 1.35

Get rid of decimals by multiplying every term by 100:

         5x + 25(11-x) = 135

        5x + 275 - 25x = 135

            -20x + 275 = 135

                  -20x = -140

                     x = 7 = the number of nickels.

The number of quarters is 11-x or 11-7 or 4 quarters.

Checking:  7 nickels is $0.35 and 4 quarters is $1.00

            And indeed $0.35 + $1.00 = $1.35
Edwin