Answer
9000 votes
Work Step by Step
The problem can be reworded to say that LaDonna needs to get $\frac{1}{3}$ of her votes from voters who are not senior citizens. Multiply the total votes needed $\frac{1}{3}$ to determine how many votes must come from voters who are not senior citizens.
$27,000 \times \frac{1}{3} = \frac{27,000}{3} = \frac{27,000 \div 3}{3 \div 3} = \frac{9,000}{1} = 9000$