A survey of 300 parks showed the following
15 had only camping
20 had only hiking trails
35 had only picnicking
185 had camping
140 had camping and hiking trails
125 had camping and picnicking
210 had hiking trails
Find the number of parks that:
Did not have any of these features?
Had exactly two of these features??
We'll be glad to check your answers.
To find the number of parks that did not have any of these features, we can add up the number of parks that had each individual feature and subtract it from the total number of parks surveyed.
According to the information given:
- 15 parks had only camping.
- 20 parks had only hiking trails.
- 35 parks had only picnicking.
- 185 parks had camping (including those that had camping as one of multiple features).
- 140 parks had camping and hiking trails.
- 125 parks had camping and picnicking.
- 210 parks had hiking trails.
Now, let's calculate the number of parks that did not have any of these features:
Total number of parks surveyed = 300
Number of parks that had camping = 185 (including those that had camping as one of multiple features)
Number of parks that had hiking trails = 210
Number of parks that had picnicking = 35
Number of parks that did not have any of these features = Total number of parks surveyed - (Number of parks that had camping + Number of parks that had hiking trails + Number of parks that had picnicking)
Number of parks that did not have any of these features = 300 - (185 + 210 + 35)
Number of parks that did not have any of these features = 300 - 430
Number of parks that did not have any of these features = -130 (But a negative value does not make sense in this context, so we can assume that there were no parks that did not have any of these features in the survey.)
Therefore, there were no parks that did not have any of these features in the survey.
Now, let's find the number of parks that had exactly two of these features:
Number of parks that had exactly two of these features = (Number of parks that had camping and hiking trails) + (Number of parks that had camping and picnicking) + (Number of parks that had hiking trails and picnicking) - 2 * (Number of parks that had camping, hiking trails, and picnicking)
Number of parks that had exactly two of these features = 140 + 125 + (Number of parks that had hiking trails and picnicking) - 2 * (Number of parks that had camping, hiking trails, and picnicking)
Now, we need to find the number of parks that had hiking trails and picnicking. We can determine this by subtracting the number of parks that had only hiking trails from the total number of parks that had hiking trails:
Number of parks that had hiking trails and picnicking = Total number of parks that had hiking trails - Number of parks that had only hiking trails
Number of parks that had hiking trails and picnicking = 210 - 20
Number of parks that had hiking trails and picnicking = 190
Now, let's find the number of parks that had camping, hiking trails, and picnicking. We can determine this by subtracting the number of parks that had only camping, only hiking trails, or only picnicking from the total number of parks that had these features in any combination:
Number of parks that had camping, hiking trails, and picnicking = Total number of parks that had camping and hiking trails and picnicking - (Number of parks that had only camping + Number of parks that had only hiking trails + Number of parks that had only picnicking)
Number of parks that had camping, hiking trails, and picnicking = 0 - (15 + 20 + 35)
Number of parks that had camping, hiking trails, and picnicking = 0 - 70
Number of parks that had camping, hiking trails, and picnicking = -70 (Again, a negative value does not make sense in this context, so we can assume that there were no parks that had camping, hiking trails, and picnicking in the survey.)
Now, let's substitute the values we found back into the equation for the number of parks that had exactly two of these features:
Number of parks that had exactly two of these features = 140 + 125 + 190 - 2 * 0
Number of parks that had exactly two of these features = 140 + 125 + 190 - 0
Number of parks that had exactly two of these features = 455
Therefore, there were 455 parks that had exactly two of these features in the survey.