ShmoopTube

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Here’s your shmoop du jour, brought to you by cats and dogs.

00:06

We wonder if they talk about it raining humans…

00:10

The ratio of dogs to cats is 6 to 5, and the ratio of cats to birds is 2 to 3.

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What is the ratio of birds to dogs?

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First of all, we’re tempted to call the humane society,

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because having that many animals in one house HAS to be against code.

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All right, so we aren’t told HOW MANY there are of each animal,

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but we do know how many there are RELATIVE to the others.

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We know, for example that for every 6 dogs, there are 5 cats.

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And for every 2 cats there are 3 birds.

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So…how do we get from dogs to birds?

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We want to get c all by its lonesome, since it appears in both ratios…

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…so instead of saying there are 2 cats for every 3 birds…

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…let’s say there is instead ONE cat for every… one and a half bird…s…

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So now we know that c equals 1 1/2.

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Now moving to our other ratio. We have 5 cats here… or 5c… so multiply 1.5 by 5

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and we get… 7.5.

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This tells us that for every 6 dogs, there are 7 1/2 birds.

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Now we have to convert that back into a manageable ratio, we can just double both numbers…

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…so if we do that we get that there are 12 dogs for every 15 birds…

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…which reduces to 4 dogs to every 5 birds.

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This question is asking for the opposite though – the ratio of birds to dogs…

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so let’s flip it around.

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Final answer is 5 to 4.

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Okay, so we STILL don’t know the size of the zoo that nutjob has in there…

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…but we’re pretty sure there’s some city ordinance about keeping a pet giraffe.

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