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When I read often quoted claims like, "It will reduce your cholesterol by 10%." Just exactly how much is 10%? 10% out of what?

I am guessing that suppose I have cholesterol of 300mg/dL and I am told this product will reduce mine by 10%, does it mean that 10% of 300mg/dL would become 270mg/dL where 10% of 300 is 30 and I subtract 30 from 300 and it becomes 270?

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You're right. Discounts in stores function similarly. – J. M. Dec 7 '11 at 3:08
thank you. I wasn't sure if it's the same formula used for discounts at stores. – netrox Dec 7 '11 at 3:26
Heh. You can treat "x% off" and "x% reduction" as synonymous. – J. M. Dec 7 '11 at 3:30
up vote 2 down vote accepted

You are doing it correctly. Another way to calculate it would be $300 \times 0.90$.

In general, if you want to see what some number $x$ reduced by $y$ % ($1 < y < 99)$ is, you do $(1-(y\times 0.01))\times x$.

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Your bounds on $y$ aren't really needed. If I reduce an amount by 200%, then I get a negative amount, which your formula gives. Similarly, if I reduce by -5%, then this is actually a 5% increase, and your formula will give the correct answer here, as well. – Austin Mohr Dec 7 '11 at 3:39
I thought the bounds would make more sense to him, but you are of course right. – user12205 Dec 7 '11 at 11:48

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