Question

Out of the 150 students at a summer camp, 72 signed up for canoeing. There were 23 students who signed up for trekking, and 13 of those students also signed up for canoeing. Approximately what percentage of students signed up for neither?

Answer 1

Approximately 45%

Explanation:

The basic way to do this would be to subtract the number of students that signed up from the total number of students, to find the number of students that didn't sign up for either.
However, we're presented with the complication "13 of those students [that signed up for trekking] also signed up for canoeing".

So, if we were to find the number of students that signed up for one of the activities, we would have to take into consideration the 13 that were signed up in both.
Adding `72 + 23` would actually count those students twice, and so we can undo this by subtracting 13 again.

Hence, the number of students signed up for an activity is
`72 + 23 - 13 = 82`
And the number of students not signed up for either is
`150 - 82 = 68`

So then 68 students signed up for neither. As a percentage, that would be
`68 / 150 * 100 = 45.333.... %`
Which can be taken as 45%