ShmoopTube

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And here's your shmoop du jour...

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If a number is tripled, and the result is halved...

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...what is the percentage increase of the resulting number relative to the original?

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Here are the potential answers...

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Alright, well this is hard because,

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they don't give us any specific numbers so we have to kinda... make stuff up.

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So if x is the mysterious number they refer to,

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X is tripled -- so we write it as 3x.

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Next it's halved -- so we write it as 3x over 2.

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The tricky part here is recognizing the NEW and OLD number in this problem...

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...which is kind of a theoretical approach to the "new minus old over old" rate of

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growth style problem.

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We just plug in the new and the old...

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...and we have 3x over 2 minus x... all over x

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We have in the numerator 3x over 2 minus x over 1, which is the same as x.

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Multiply top and bottom here by 2 and we have 2x over 2 so now we get x over 2;

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Now divide it by x which is x over 1 And dividing by a fraction is the same as

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multiplying by the reciprocal...

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So we have x over 2x which is 1 half.

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A quick scan of the answers and boom 50% is right there --

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and the answer is A.

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