Average and Percent

Question

In an Math Exam there are 80 more men than women. The result showed that the women's average is 20% higher than men's, and that the total average is 75%. what is the women's average? So far I did ... $$H=W+80$$ $$\overline{W}=1,2\overline{H}\Rightarrow \overline{H}=\frac{\overline{W}}{1,2}$$
but $$\overline{H}=\frac{S_H}{H}\Rightarrow S_H=H\overline{H}$$ and $$\overline{W}=\frac{S_W}{W}\Rightarrow S_W=W\overline{W}$$

as $$75\%=\frac{S_W+S_H}{H+W}\Rightarrow 75\%=\frac{W\overline{W}+(W+80)\frac{\overline{W}}{1,2}}{2W+80}$$ I've tried but I couldn't handle the math till the end.

Answer 1

You don't have enough information to answer the question. If there are millions of people taking the exam, the excess of $80$ won't matter and the women score $85\%$ and the men score $65\%$. If there was $1$ woman and $81$ men the woman scored $777/820\approx 94.756\%$ and the men averaged $613/820\approx 74.756\%$. Both satisfy the conditions of the problem.

Answer 2

$W$, average score from the women.

$M$, average score of the men.

$x$, total number of female students.

$x+80$, total number of male students

$$ \frac{M(x+80)+W(x)}{x+(x+80)}=.75 $$

$$ W=.2+M $$

$$ (W-.2)(x+80)+xW=.75(2x+80) $$

$$ xW+80W-.2x-16+xW=1.5x+60 $$

$$ W(2x+80)=1.7x+76 $$

$$ W=\frac{1.7x+76}{2x+80} $$

You need to know how many female students there are in this class to answer this question.