SOLUTION: john has a total of 13 coins in his pocket. of the 13 coins they are all either quarters or dimes. the total value of the coins is $2.50. how many quarters does john have in his po

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Question 934184: john has a total of 13 coins in his pocket. of the 13 coins they are all either quarters or dimes. the total value of the coins is $2.50. how many quarters does john have in his pocket?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
john has a total of 13 coins in his pocket. of the 13 coins they are all either
quarters or dimes. the total value of the coins is $2.50. how many quarters does
john have in his pocket? 
Let the number of nickels be x
Then the number of dimes, using 
ONE PART = TOTAL MINUS OTHER PART,
is 13-x.  
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
QUARTERS     x        $0.25    $0.25x 
DIMES      13-x       $0.10    $0.10(13-x)
-------------------------------------------
TOTALS      13        -----    $2.50

 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%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccoins%29%29

0.25x + 0.10(13-x) = 2.50

Get rid of decimals by multiplying every term by 100

     25x + 10(13-x) = 250

    25x + 130 - 10x = 250

          15x + 130 = 250

                15x = 120

                  x = 8 = the number of quarters

The number of dimes is 13-x or 13-8 or 5 dimes.

Checking:  8 quarters is $2.00 and 5 dimes is $0.50

And indeed $2.00+$0.50 = $2.50.

Edwin