SOLUTION: Robyn's piggy bank contains fifty coins in dimes and quarters. The coins have a total value of $8.60. Find the number of dimes and quarters in the piggy bank.

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Question 918248: Robyn's piggy bank contains fifty coins in dimes and quarters. The coins have a total value of $8.60. Find the number of dimes and quarters in the piggy bank.
Answer by Edwin McCravy(20056) 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 50-x. 

Make this chart:

                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
DIMES         x        $0.10    $0.10x 
QUARTERS    50-x       $0.25    $0.25(50-x)
-------------------------------------------
TOTALS       50        -----    $8.60

 %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(50-x) = 8.60
Get rid of decimals by multiplying every term by 100
     10x + 25(50-x) = 860   
   10x + 1250 - 25x = 860
        -15x + 1250 = 860
              -15x = -390
                 x = 26 = the number of dimes
The number of quarters is 50-x or 50-26 or 24 quarters.

Checking: 26 dimes + 24 quarters = 50 coins. That checks.
26 dimes is worth $2.60 and 24 quarters is worth $6.00.
That adds to $8.60.  That checks.  So we are right.

Edwin