In a street, a survey showed that out of a hundred households 60 had a cat, 40 had a dog, and 20 had neither a cat nor a dog.

How many households had a cat but no dog?

A. 20

B. 50

C. 40

D. 10

E. 30

In a street, a survey showed that out of a hundred households 60 had a cat, 40 had a dog, and 20 had neither a cat nor a dog.

How many households had a cat but no dog?

A. 20

B. 50

C. 40

D. 10

E. 30

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Simple steps to solve word problems:

- Underline key information
- Determine what they are trying to ask, and what you will need to solve it

Eliminate any non-essential information - Draw a picture, graph, or equation

In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes. - Solve.

The first thing we want to do is eliminate the households without a cat or dog from the total. We can do this by taking the total number of households minus the number without any cats or dogs.

100-20=80

We want to do this because it leaves us with only houses that have cats, dogs, or both. From this we can calculate cats only.

Cats (60) + Dogs (40) = 100

We have 100 cats and dogs total spread across 80 different households. We can take the difference between the two to find the overlap, meaning which houses have both a cat and a dog.

100 - 80 = 20

So 20 houses have both a cat and a dog.

Finally, we can take this number to find the number of cats only houses.

Total cats - number of cats in a cat and dog home = Households with a cat but no dog

60-20=40

\fcolorbox{red}{grey!30}{Therefore the answer is C, $40$.}

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