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  into : .