Table: golf_tournament_results_3
Columns: year
winner
country
score
to_par
1st_prize

Question: What is the total number of 1st prize ($) that has a United States country with a score lower than 271 and in a year after 1964 with a winner of Bobby Mitchell?
SQL: SELECT COUNT("1st_prize") FROM golf_tournament_results_3 WHERE "country" = 'united states' AND "score" < 271 AND "year" > 1964 AND "winner" = 'bobby mitchell'