The George Washington Carver - Booker T Washington Half Dollars were authorized on September 21, 1951 via an amendment to the original Booker T. Washington Birthplace Memorial Coin Act of August 7, 1946. The first batches of GWC-BTW coins were struck at the Mints of the United States in December 1951: 110,000 in Philadelphia, plus 10,000 each in Denver and San Francisco. (In addition, there were 18 coins struck for assay purposes in Philadelphia, and four each in Denver and San Francisco,)
1951 George Washington Carver-Booker T Washington Half Dollar
George Washington Carver
George Washington Carver died on January 5, 1943. In 1945, during the 79th Congress, Joint Resolutions were introduced in the House and Senate that called for January 5, 1946 to be "designated as George Washington Carver Day, in commemoration of the great scientist." US President Harry S. Truman signed the House version of the Joint Resolution into law on December 28, 1945 (Public Law 79-290) and issued Proclamation 2677 that declared "it is fitting that we honor the memory of George Washington Carver who contributed to the expansion of the agricultural economy of the nation through his diligent research as an agricultural chemist." (Note: The Senate version of the Joint Resolution remained in Committee in lieu of the House version.)
Though the Public Law and Presidential Proclamation were specific to January 5, 1946, the day has continued to be recognized as George Washington Carver Day by some.
Carver was honored on a US postage stamp in 1948:

In January 1952, the day (January 5) served as the official kick-off date for sales of the new coin. A contemporary Press Release from the Booker T. Washington Birthplace Memorial stated, "We have dedicated a new coin to the memory of Dr. Carver, and it is both fitting and proper that January 5th, which is National Carver Day, inaugurate this historical event."
Individual coins from the Philadelphia Mint were priced at $3.00 each, with three-coin P/D/S Sets being offered at $10.00 per Set. Per the coin's legislation, net proceeds from the sale of the coins was to be used "to oppose the spread of communism among Negroes in the interest of the national defense."
These coins would be the only GWC-BTW half dollars dated "1951" issued as the next run of coins, struck in March, were dated "1952".
For a closely related "Sales Kickoff" story, see:
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Quick Bits #40 - 1951 George Washington Carver - BTW Half Dollar LaunchFor other of my posts about commemorative coins and medals, including more BTW-GWC half dollar stories, see:
Commems Collection.