A fractions problem - Cats?

Question

At a Cats Galore Cat Show, 1/2 of the cats were Siamese, 1/4 were Persian, 1/5 were Abbys, and one cat was a Tabby.
How many cats were in the show?
How many were Siamese?
How many were Persian?
How many were Abbys?
How did you find your answer?

Answer 1

One tabby, 4 Abby's, 5 Persians, and 10 Siamese, with 20 cats in all. This is all under the assumption that the one Tabby cat makes up for the missing fraction of the cats. To find this answer, convert the other fractions so they have a common denominator. In this case, 20. *** the numerators, and you get 19. THis means the one Tabby makes up one 20th, which makes it easier for us. The answer for the other cats is merely the numerator.

Answer 2

Meow.

I have no idea. We could have 50 Siamese, 25 Persians, 20 Abbys (Abbysinian, I take it), 1 Tabby, and 4 Tuxedo kitties and that would meet the conditions of the problem. Or we could have 500 Siamese, 250 Persians, 200 Abbys, 1 Tabby, 25 Russian Blues, and 24 domestic short hairs and that would meet the conditions.

I will make the condition that there are no breeds of cats there other than those you mention. Let the total number of cats be P (for purr). Then

(1/2)P + (1/4)P + (1/5) P + 1 = P

Or [ 1/2 + 1/4 + 1/5] P + 1 = P

Oh, my. Fractions. Find common denominators. Maybe decimals would be quicker:

(0.5 + 0.25 + 0.2)P + 1 = P
0.95P + 1 = P
1 = (1-0.95) P
1 = 0.05 P
P = 20

Fortunately the answer turned out to be an integer, because half a kitty could only make half a meow. So the answer to the first question was 20. Half of them, or 10, were Siamese. There were 5 Persians, 4 Abbys, and 1 Tabby.

I'm not certain whether telling you how to do it helps, so I will give you another problem, a dog show. At a dog show, 1/2 the dogs were collies, 1/3 were German shepherds, 1/9 were malamutes, and 1 dog was a mutt. There were no other types of dogs. How many of each were there, of which type?

Answer 3

1/2 + 1/4 + 1/5 = 19/20

20 cats were in the show, 10 Siamese, 5 Persian, 4 Abbys

Answer 4

First, find the common denominator:
1/2=10/20 1/4=5/20 1/5=4/20, then add 'em up:
10/20 + 5/20 + 4/20 = 19/20
The one tabby cat must be the 1/20 that makes up the whole group of cats.
Therefore, there are 20 cats in the group.
Siamese =1/2 * 20 or 10
Persian = 1/4 * 20 or 5
Abbys = 1/5 * 20 or 4
And the remaining single Tabby makes 20.

Answer 5

1/2 + 1/4 + 1/5 = 10/20 + 5/20 + 4/20 = 19/20

So there were 20 cats, of which 10 were Siamese, 5 where Persian, and 4 were Abbys.

Answer 6

1/2 + 1/4 + 1/5 = 19/20

20 cats were in the show
10 Siamese
5 Persian
4 Abbys

Answer 7

let the total numberbe x
x=1/2x+1/4x+1/5x+1
x=(10+5+4)*x/20+1
20x=19x+20
x=20
so there were 10 siamese,5 persian 4 abbys and 1 tabby
total cats in the show=20

Answer 8

The smallest number answers to this question are:
20 cats
10 siamese
5 Persian
4 Abby
1 Tabby

The answer just sort of comes to you; it's hard to say how, exactly. But remember, there is no mention of other types of cats; that doesn't mean other types aren't in the show. So there could, theoretically, be any number (higher than 20) of cats in the show.

Answer 9

20


10
5
4
+1
---
20

Answer 10

I only do dogs.