Emily's quiz scores so far are: 92, 95, 87, 89 and 100. What score does she need to get on the sixth quiz to make the arithmetic mean of the six scores equal 93?
Subtract 90 from every score to simplify the arithmetic.  For the average of 6 scores to be 3, their sum must be $6\times3=18$.  The sum of her first five scores is $2+5-3-1+10=13$, so the sixth score should be $18-13=5$.  Adding 90 back, her score should be $\boxed{95}$.