# 35 students took part in freestyle swimming event. 23 took part in the backstroke event and 10 students took part in both. How many students in total took part in the event?

Mar 11, 2018

Number of students who took part in the event is $48$.

#### Explanation:

To find total number of students, we should add

1. Those who participated only in freestyle swimming event,
2. Those who participated only in backstroke swimming event
3. Those who participated in both the swimming events (note they are not included in $1$ and$2$ above)

Now, as $23$ students took part in backstroke event and $10$ students took part in both i.e. backstroke as well as freestyle, $23 - 10 = 13$ students participated only in backstroke event.

Similarly, as $35$ students took part in freestyle event and $10$ students took part in both i.e. backstroke as well as freestyle, $35 - 10 = 25$ students participated only in backstroke event.

Hence number of students who took part in the event is $25 + 13 + 10 = 48$.