Problem Solving, Problem Solving, Problem Solving?

Draw a Venn diagram with overlapping circles

for runners (R) and swimmers (S).

20 are in the intersection, so 50 - 20 = 30 are just runners,

and 67 - 20 = 47 are just swimmers.

So 20 + 30 + 47 = 97 run or swim or both.

So 100 - 97 = 3 do neither.

It would be easier to set up a venn diagram, but since i cant do that here i'll try to describe it. In the intersection, there would be 20, and since those people are runners and swimmers we would subtract 20 from 50 and 67, so there is 30 in the runners only section, and 47 in the swimmer only section. Now we add up 30 + 47 + 20 = 97, then do 100 - 97 = 3.

So there are 3 athletes who are neither runners nor swimmers.

You have 100 athletes,

You have 50 runners and 67 swimmers. 50 + 67 = 117.

20 athletes both run and swim 117-20 = 97

So the total of athletes who are runners and swimmers or both is 97

That leaves 3 athletes who do neither.

Hi,

100 athletes - (50 runners + 67 swimmers - 20 duplicates) =

100 - (50 + 67 - 20) = 100 - 97 = 3

3 athletes are neither swimmers nor runners. <==ANSWER

I hope that helps!! :-)

No of athletes who are runners but not swimmers = 50 -20 = 30 --------------------- (1)

No of athletes who are swimmers but not runners = 67 -20 = 47 ---------------------(2)

No of athletes who are bot runners and swimmers = 20 (given) ----------------------(3)

Required No of athletes who are neither runners nor swimmers = 100 -(30+47+20) = 3

100- 20 = 80

50 - 20 = 30

67 -20 = 47

80 - ( 30+7) = 3 ANSWER