Question 925310
{{{drawing(400,400,-3,3,-2,4,
blue(circle(-1,0,1.5)),
red(circle(1,0,1.5)),
green(circle(0,1.8,1.5)),
locate(-1.1,0,x),locate(1,0,x),
locate(0,1.8,x),locate(-0.05,0.75,3),
locate(-0.8,1.1,y),locate(0.7,1.1,y),
locate(0,-0.1,y),locate(-0.4,3.6,green(hiking)),
locate(-2,-1.55,blue(walking)),locate(0.8,-1.55,red(jogging))
)}}} 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+3y+3=30}}} because there is a total of 30 people.
{{{y=(1/2)x}}}<--->{{{x=2y}}} because half as many people enjoy exactly two of theses activities as those who enjoy only one activity.
So {{{3(2y)+3y+3=30}}}
{{{6y+3y+3=30}}}
{{{9y+3=30}}}
{{{9y=30-3}}}
{{{9y=27}}}
{{{y=27/9}}}
{{{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*3}}}--->{{{x=6}}} , meaning that there are 6 people who enjoy just one of the 3 activities.
{{{drawing(400,400,-3,3,-2,4,
blue(circle(-1,0,1.5)),
red(circle(1,0,1.5)),
green(circle(0,1.8,1.5)),
locate(-1.1,0,6),locate(1,0,6),
locate(0,1.8,6),locate(-0.05,0.75,3),
locate(-0.8,1.1,3),locate(0.7,1.1,3),
locate(0,-0.1,3),locate(-0.4,3.6,green(hiking)),
locate(-2,-1.55,blue(walking)),locate(0.8,-1.55,red(jogging))
)}}}
From the circles, you see that the people who enjoy jogging are
{{{x+y+y+3=6+3+3+3=highlight(15)}}}
 
NOTE:
The kind of drawing where we use circles (or ovals to represent groups of things is called a Venn diagram.