# How to express the result in terms of fifths?

In a school, the number of girls exceeds in its third part, the number of boys.

Is it correct that, boys are $\frac{2}{5}$ of total students?

$g =$ girls

$b = b$

$g = b + \frac{1}{3}g$

$\frac{2}{3}g = b$ and $\frac{3}{2}b = g$

The total amount of students, in function of girls are:

$\frac{2}{3}g + g = \frac{5}{3}g$

The total amount of students, in function of boys are:

$\frac{3}{2}b + b = \frac{5}{2}b$

Well up here, I have all the quantities.

But none in terms of $\frac {2} {5}$, then what should I do?

• I can understand the translation of "the number of girls exceeds in its third part, the number of boys" as the class is $\frac 35$ girls and $\frac 25$ boys although I have never heard the expression before. Everything you have done after that is fine. You did not give us the question you were asked, so it is not clear what you are looking for or what answer is expected from you. Why does it need to involve $\frac 25$? What is the question? – Ross Millikan Mar 10 '18 at 23:57

As you said:

“The total amount of students, in function of boys are:

$\frac{3}{2}b + b = \frac{5}{2}b$ ”

Let $T$ be the total number of students.

Then your words mean $$T= \frac{3}{2}b + b = \frac{5}{2}b$$

So we have $$T=\frac{5}{2}b$$ $$b=\frac{2}{5}T$$

The boys are $\frac{2}{5}$ of the total.

• Thanks, perfect and clear. – Eduardo S. Mar 11 '18 at 18:42