The question states the following:
Helen's score on a final test in a certain course was 60 percent greater than her average (arithmetic mean) score of the 2 other tests taken in the course. Helen's score on the final test was what percent of the student's average test score for the entire course?
I solved this by setting up the following equations:
$f$ = score on the final test $a+b$ = sum of scores on the first two tests
So, given the information in the problem, I set up the following equations:
$$f=1.6*\frac{a+b}{2}$$ $$f=x*\frac{a+b+f}{3}$$
where $x$ is obviously the answer that we're seeking: the percentage (as a decimal) of the average for the entire course.
Solve for $a+b$ and get $a+b=\frac{f}{0.8}$. Plugging that into the second equation I get the following:
$$f=\frac{\frac{f}{0.8}+f}{3}x$$
And solving for $x$ I'm getting $x=6/7$.
But this is not the correct answer.
Can someone please point out where my logic is incorrect?
Thanks.
Making a third score $60\%$ greater than the average of the first two scores will increase the average by $\frac{60\%}{3} = 20\%$
IOW, new average $= \frac{100 + 100 +160}{3}$ which is $120\%$ of the old average.
$\frac{160}{120} = \frac{4}{3}$ which is $133.333\%$