What is the retained earnings if:
Total Assets 12/31/2009 $155,000
Total Liabilities 12/31/2009 $75,000
Paid-in capital 12/31/2009 $45,000
Retained earnings, 12/31/09 $35,000
Net income for 2009 $25,000
Dividends declared and paid during 2009 $16,500
Retained Earning ending, 1/1/09 is what??

Retained Earning ending, 1/1/09 is :-
$ 26,000.

A - L = 80,000 -45,000 = 35,000.

Total Equity is also = 35,000.

Open as above = 26,000
add income ***= 25,000
-------------------------
sub-total******=51,000
less dividends **=16,000
---------------------------
Total Equity****= 35,000
==================

Opening balance in the retained earnings is $26,500:

Ending balance $35,000
Dividends paid 16,500
Net Income for the year (25,000)
Opening balance $26,500

Retained Earning ending, 1/1/09 is :-
$ 26,000.

A - L = 80,000 -45,000 = 35,000.

Total Equity is also = 35,000.

Open as above = 26,000
add income ***= 25,000
-------------------------
sub-total******=51,000
less dividends **=16,000
---------------------------
Total Equity****= 35,000
==================

It is the first time I have seen a retained earnings balance referred to as Total Equity.

Please re read the question and that too carefully. The total assets are not $80,000 as you have stated. It represents net assets. The total equity is the capital + retained earnings or net assets