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The demand equation for the Olympus recordable compact disc is $100x^2 + 9p^2 = 3600$ where x represents the number (in thousands) of 50-packs demanded per week when the unit price is p dollars. How fast is the quantity demanded increasing when the unit price per 50-pack is 12 dollars and the selling price is dropping at the rate of 11¢ per 50-pack per week? (Round your answer to the nearest integer.) So this is what i have so far $$p=12$$$$x=4.8$$ $$\frac{dp}{dt}=-.11$$ so $$200x\frac{dx}{dt}+18p\frac{dp}{dt}=0$$ Subtituting for $x,p$ and $\frac{dp}{dt}$ I got $$960\frac{dx}{dt}+216(-.11)=0$$$$=$$ $$\frac{dx}{dt}=\frac{23.76}{960}=.02475$$ which isn't the correct answer so I am wondering where I am going wrong and what are the right steps to take, all help is appreciated.

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  • $\begingroup$ What is the expected answer? $\endgroup$ – mfl Jun 30 '14 at 1:29
  • $\begingroup$ Not sure, but per the instruction at the very least an integer that isn't a 0. With my answer I round to 0 and it was marked wrong.@mfl $\endgroup$ – Kenshin Jun 30 '14 at 1:30
  • $\begingroup$ @Kenshin where are you getting your value of x? I think that value is incorrect and is what is causing your error $\endgroup$ – Varun Iyer Jun 30 '14 at 1:31
  • $\begingroup$ @VarunIyer I'm solving for x out of the original equation. $100(4.8)^2+9(12)^2=3,600$ I don't know whether that's right or not though.. $\endgroup$ – Kenshin Jun 30 '14 at 1:33
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    $\begingroup$ The given answer explains it. $\endgroup$ – mfl Jun 30 '14 at 1:39
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The problem said $x$ is the number of 50-packs per week in thousands, that is, the demand is $1000x$ 50-packs per week. Personally I think this is adding just a little bit too much "realism" to the question (yes, in business people often make tables in which one column is "in thousands" or even "in millions", but what is wrong with writing it as "$1000x$" when it's a calculus exercise?), and I missed it myself on the first reading (maybe the second too).

Since the question asks you to round the answer to the nearest integer, I suppose they mean the answer to be in terms of single units (each unit being a 50-pack!), so we take your answer (which as far as I can see is the correct value of $x$), multiply by $1000$, and round to an integer. Does that give you the correct answer?

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  • $\begingroup$ Yes!! It was 25 (24.75 rounded up) I guess it is the wording that threw me off. Reading is fundamental, haha! Thanks so much! $\endgroup$ – Kenshin Jun 30 '14 at 1:39

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