SOLUTION: In a survey, 30 people reported that they enjoy some combination of walking, hiking, and jogging. The number who enjoy only walking, the number who enjoy only hiking, and the numbe

Algebra ->  Circles -> SOLUTION: In a survey, 30 people reported that they enjoy some combination of walking, hiking, and jogging. The number who enjoy only walking, the number who enjoy only hiking, and the numbe      Log On


   

Question 925310: In a survey, 30 people reported that they enjoy some combination of walking, hiking, and jogging. The number who enjoy only walking, the number who enjoy only hiking, and the number who enjoy only jogging are all equal. Likewise, the number who enjoy only walking and hiking, the number who enjoy only walking and jogging, and the number who enjoy only hiking and jogging are equal. In addition, the survey showed that half as many people enjoy exactly two of theses activities as those who enjoy only one activity. If three people enjoy all three activities, how many people enjoy jogging?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Each circle represents the number of people who engage in each activity.
x= number of people who enjoy only 1 of the 3 activities.
y= number of people who enjoy only 2 of the 3 activities.
3= number of people who enjoy all 3 activities.

3x%2B3y%2B3=30 because there is a total of 30 people.
y=%281%2F2%29x<--->x=2y because half as many people enjoy exactly two of theses activities as those who enjoy only one activity.
So 3%282y%29%2B3y%2B3=30
6y%2B3y%2B3=30
9y%2B3=30
9y=30-3
9y=27
y=27%2F9
y=3 There are 3 people who enjoy only walking and hiking, another 3 who enjoy only walking and jogging, and yet another 3 who enjoy only hiking and jogging.
Also x=2%2A3--->x=6 , meaning that there are 6 people who enjoy just one of the 3 activities.

From the circles, you see that the people who enjoy jogging are
x%2By%2By%2B3=6%2B3%2B3%2B3=highlight%2815%29

NOTE:
The kind of drawing where we use circles (or ovals to represent groups of things is called a Venn diagram.