Answer:
$291,460
Step-by-step explanation:
Data provided in the question: 
Purchasing cost of the personal residence = $295,000
Real estate tax paid by Alice before the sale = $4,425
Property tax allocated to Alicia = $885 
Property tax allocated to Rick = $3,540
Now,
Rick's basis in the residence will be 
= Purchase cost - Property taxes allocated to Rick 
= $295,000 - $3,540
= $291,460