SOLUTION: anothony has a total of 30 dimes and quarters worth $5.70. how many of each type of coin does he have

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Question 822105: anothony has a total of 30 dimes and quarters worth $5.70. how many of each type of coin does he have
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of dimes be x
Then the number of quarters, using ONE PART = TOTAL MINUS OTHER PART,
is 30-x.  

                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
DIMES         x        $0.10    $0.10x 
QUARTERS    30-x       $0.25    $0.25(30-x)
-------------------------------------------
TOTALS       30        -----    $5.70 

The equation comes from the column on the right

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

0.10x + 0.25(30-x) = 5.70

Get rid of decimals by multiplying every term by 100

    10x + 25(30-x) = 570
   10x + 750 - 25x = 570
        -15x + 750 = 570
              -15x = -180
                 x = 12 = the number of dimes

The number of quarters is 30-x or 30-12 or 18 quarters.

Edwin