Question

A class consists of 1/5 freshmen, 3/5 sophomores, and 1/10 juniors; the rest are seniors. what fraction of the class is seniors?

Answer 1

The sum of freshmen, sophomores, juniors and seniors must be 1, because 1 corresponds to 100%, then we can write:

$\frac{1}{5}+\frac{3}{5}+\frac{1}{10}+x=1$

where x denotes the seniors. This last equation is equivalent to

$\frac{4}{5}+\frac{1}{10}+x=1$

Now, we will add the fraction on the left hand side,

$\frac{4}{5}+\frac{1}{10}=\frac{8}{10}+\frac{1}{10}=\frac{9}{10}$

then, our equation is

$\frac{9}{10}+x=1$

By moving 9 over 10 to the right hand side, we get

$x=1-\frac{9}{10}$

then, x is given by

$\begin{gathered} x=\frac{10}{10}-\frac{9}{10} \\ x=\frac{1}{10} \end{gathered}$

then, the fraction of seniors is 1/10