1951 is not a rare year for Washington quarters. 1964 and earlier quarters are 90% silver. In average condition their retail value is about 0.18 X the current price of silver; a metal dealer will pay less.
If the coin is in better shape look on the back to see if there's a small mint mark letter below the bow in the wreath. It may be blank or there may be a D or S.
Numismedia lists the following approximate retail values as of 01/2013:
No mint mark (Philadelphia):
Almost no wear - $7.30
Uncirculated - $8.91 to $3130.00 depending on quality
"D" mint mark (Denver):
Almost no wear - $7.30
Uncirculated - $8.91 to $412.50
"S" mint mark (San Francisco):
Almost no wear - $8.20
Uncirculated - $13.23 to $3280.00
DISCLAIMER: The retail values quoted are the best available as of the date shown, but may vary due to market fluctuations. Also the wholesale (buying) price of a coin will be less than the selling (retail) price. A reputable coin dealer will be able to give a more accurate valuation based on inspection of the coin.
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