Asked by Anne
The are 99 dogs. 49 bark consistently while 69 whines. 29 dogs both whine and bark. How many of the dogs neither whine nor bark?
Answers
Answered by
Reiny
Best illustrated with a Venn diagram.
Draw two intersecting circles, label one barking, the other whining.
place 29 in the intersection of the two circles
In the non-intersecting part of the barking circle place 49-29 or 20
In the non-intersecting part of the whining circle place 69-29 or 40
Add the numbers you see in your circles:
40+29+20 = 89
but you had 99 dogs, so 10 would not be in either the barking or whining circles
- they neither bark nor whine
or
Number(bark or whine) = number(bark) + number(whine) - number(bark AND whine)
= 49+69-29 = 89
leaving 10 not accounted for.
Draw two intersecting circles, label one barking, the other whining.
place 29 in the intersection of the two circles
In the non-intersecting part of the barking circle place 49-29 or 20
In the non-intersecting part of the whining circle place 69-29 or 40
Add the numbers you see in your circles:
40+29+20 = 89
but you had 99 dogs, so 10 would not be in either the barking or whining circles
- they neither bark nor whine
or
Number(bark or whine) = number(bark) + number(whine) - number(bark AND whine)
= 49+69-29 = 89
leaving 10 not accounted for.