1 basketball and 2 football * * * need 60.20 yuan;

Therefore, three basketballs and six footballs * * * need 60.20*3= 180.60 yuan (2).

Note that (2)-( 1)= the price of a football =180.60-164.90 =15.70 (yuan).

Therefore, the price of a basketball =60.20- 15.70*2=28.80 (yuan).