Question

a survey of 240 families revealed the following information.
91 had a dog
70 had a ca
31 had a dog and a cat
91 had neither a cat nor a dog nor a parakeet
7 had a cat, a dog, and a parakeet

How many had a parakeet only?

Answer 1

supposed to use a venn diagram to solve the question about the parakeet

Answer 2

no, that's only the tri-section
you have to do some math to figure out the left-overs and therefore the amount of people who had a parakeet

Answer 3

This situation might look something like this

Answer 4

however, I'm not too sure about whether the 91 for the dogs and the 70 for the cats includes the 31 and 7 already or not ...

Answer 5

ok, so I think that the 31 and 7 numbers are a part of the 91 and 70 so let me edit the venn diagram

Answer 6

\(\color{#0cbb34}{\text{Originally Posted by}}\) Angle
no, that's only the tri-section
you have to do some math to figure out the left-overs and therefore the amount of people who had a parakeet
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 7

Ok

so the math that we need to do for this problem @joeellison will be:
Total number of families = 240
minus the ones that don't have any pets = 91
minus the families that do have dogs = 91
minus the families that do have cats = 70
add back the overlap of dogs and cats = 31

Answer 8

that number 31 I think should be 24 because it's 31-7 and its good to label each empty space that the three circles form. they're referred to as "regions"

Answer 9

\(\color{#0cbb34}{\text{Originally Posted by}}\) Angle
Ok

so the math that we need to do for this problem joeellison will be:
Total number of families = 240
minus the ones that don't have any pets = 91
minus the families that do have dogs = 91
minus the families that do have cats = 70
add back the overlap of dogs and cats = 31
add back the overlap of dogs cats parakeets = 7
\(\color{#0cbb34}{\text{End of Quote}}\)

240 - 91 - 91 - 70 + 31 + 7
^ this math will give us the families that ONLY have parakeets

Answer 10

I don't know how to do that though. So the upper right circle could be labeled r1, the left circle, r3 and where your 31 is would be r2 and the little overlap region just below r2 would be r4, so your just kind of going right to left. The bottom circle would be r7 and the overlaps would be r5 and r6

Answer 11

like this you mean?

Answer 12

here is how you could think about it:

If you want to figure out "How many people have dogs or cats?"
You would do: r1 + r3 - r2 - r4

We added dog + cat minus overlap

Answer 13

Then to figure out the families that have only parakeets:
` Total surveyed ` minus ` people who don't have pets ` minus ` people who have (dogs OR cats) `

Answer 14

yes, and you can label the upper right dog, the left cat and the bottom circle parakeet to help keep things organized

Answer 15

\(\color{#0cbb34}{\text{Originally Posted by}}\) Angle
\(\color{#0cbb34}{\text{Originally Posted by}}\) Angle
Ok

so the math that we need to do for this problem joeellison will be:
Total number of families = 240
minus the ones that don't have any pets = 91
minus the families that do have dogs = 91
minus the families that do have cats = 70
add back the overlap of dogs and cats = 31
add back the overlap of dogs cats parakeets = 7
\(\color{#0cbb34}{\text{End of Quote}}\)

240 - 91 - 91 - 70 + 31 + 7
^ this math will give us the families that ONLY have parakeets
\(\color{#0cbb34}{\text{End of Quote}}\)

so I stand by what I said before that this is the math you would to do get the answer to your problem

Answer 16

actually i told you backwards about the regions-the upper r1 starts in the upper left, then you go left to right, but it'll work this way anyway I thiink

Answer 17

yup :)

Answer 18

I've gtg, but you can tag @ AZ if you need to check your answer or if you get stuck

Answer 19

k thanks