Posted by **Lisa** on Tuesday, April 15, 2008 at 2:25pm.

In a community of 416 people, each person owns a dog or a cat or both. If there are 316 dog owners and 280 cat owners, how many of the dog owners own no cat?

The choices are:

36

100

136

180

316

I think the answer is either 180 or 316, but I'm not sure.

- math -
**Reiny**, Tuesday, April 15, 2008 at 2:43pm
Do it with Venn diagrams

draw two intersecting circles, label the overlap as x

This will represent the people owning both cats and dogs

label one circle D for dogs, the other C for cats

label the part of circle D without the overlap as 316-x

label the part of the circle C without the overlap 280-x

now 316-x + x + 280-x = 416

x = 180

so the dog owners owning "no cat" would be those in the D circle outside the overlap or 316-x = 316-180 = 136

- math -
**Lisa**, Tuesday, April 15, 2008 at 2:50pm
Thank you.

- math -
**marlene**, Tuesday, April 15, 2008 at 7:41pm
how do you round

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