Question

There are 135 people in a sport centre.
77 people use the gym.
62 people use the swimming pool.
65 people use the track.
27 people use the gym and the pool.
23 people use the pool and the track.
31 people use the gym and the track.
4 people use all three facilities.
How many people use at least two facilities?

Answer 1

Answer:

Given:

There are 135 people.

There are 3 facilities - Gym, Swimming Pool and Track.

Gym = 77

Swimming Pool = 62

Track = 65

Gym and pool = 27

Pool and track = 23  

Gym and track = 31

All 3 facilities = 4

To Find:

The number of people who use exactly one facilities.

Explanation:

Such question is easiest solved by using a Venn diagram. See attached.

Solution:

Find the number of people who goes to Gym and Swimming Pool only:

Gym and Swimming Pool only = 27 - 4

Gym and Swimming Pool only = 23

Find the number of people who goes to Swimming Pool and Track only:

Gym and Swimming Pool only = 23 - 4

Gym and Swimming Pool only = 19

Find the number of people who goes to Gym and Track only:  

Gym and Swimming Pool only = 31 - 4

Gym and Swimming Pool only = 27

Find the number of people who goes to Gym only:

Gym only = 77 - 23 - 27 - 4

Gym only = 23

Find the number of people who goes to Swimming Pool only:

Swimming Pool only = 62 - 23 - 19 - 4

Swimming Pool only = 16  

Find the number of people who goes to Track only:

Track only = 65 - 27 - 19 - 4

Track only = 15

Find the total number of people who goes to one facility only:

One Facility = 23 + 16 + 15

One Facility = 54  

Answer: 54 people

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