234k views
0 votes
In a survey of 97 resorts, it was found that:

31 had a spa
39 had a children's club
12 had a spa and children's club
8 had all three features
62 had a fitness center,
17 had a spa and a fitness center,
19 had a fitness center and children's club.
a) How many of the resorts surveyed had only a spa?

1 Answer

6 votes

Final answer:

Out of the 97 resorts surveyed, 10 had only a spa. This was calculated by subtracting the number of resorts with additional features (spa and children's club or spa and fitness center) from the total number that had spas, and then adding back the resorts with all three features.

Step-by-step explanation:

To find out how many of the resorts surveyed had only a spa, we need to consider the numbers provided for the combinations of features and then perform some calculations to isolate the number of resorts with just a spa. Here's a step-by-step breakdown:

  • Total resorts with at least a spa: 31
  • Total resorts with both spa and children's club: 12
  • Total resorts with all three features (spa, children's club, and fitness center): 8
  • Total resorts with both spa and fitness center: 17

To calculate the number of resorts with only a spa, subtract the number of resorts that have a spa combined with other features from the total number of resorts with spas. So:

Only spa = Total spa - (Spa & children's club + Spa & fitness center) + Resorts with all three features because they have been subtracted twice in the previous step.

The calculation would be:

Only spa = 31 - (12 + 17) + 8

Only spa = 31 - 29 + 8

Only spa = 2 + 8

Only spa = 10

Therefore, 10 resorts had only a spa, without any other feature like a children's club or fitness center.

User Derek Prior
by
8.0k points