Hello, mr.toronto!

The teacher gives the following homework assignment: You have to write an essay.

You may work alone or in boy-girl pairs.

As it turned out, 2/3 of the boys and 3/5 of the girls worked in pairs.

What fraction of the class worked alone?

Let = number of boys in the class.

Let = number of girls in the class.

\. . Then there are students in the class.

2/3 of the boys worked in pairs:

They paired off with 3/5 of the girls:

. . Hence: .

Then 1/3 of the boys worked alone: .

. . and 2/5 of the girls worked alone: .

The fraction of students working alone is: .

Substitute [1] into [2]: .