Question

If a third of the students entering high school drop out before graduating, but three-fifths eventually return and get their diploma, what proportion of students entering high school eventually get their diplomas?

Answer 1

`(13)/(15)`

Explanation:

If a third drop out, Initial fraction of those who graduate =
`1-(1)/(3) =(2)/(3)`

Three-fifths of those who dropped out(one third) eventually return =
`(3)/(5) of (1)/(3) =(3)/(5) X (1)/(3)=(1)/(5)`

The proportion of students entering high school who eventually graduate

= Those who graduated Initially+Those who returned

=
`(2)/(3)+(1)/(5)=(10+3)/(15)=(13)/(15)`