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## anonymous 5 years ago The sum of a number and twice another number is 12. What is their maximum product?

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1. anonymous

hello!!! suppose the number be x so the other number will be 2x so according to question x + 2x = 12 3x = 12 x = 4 so 2x = 8 product = 8 * 4 = 32 this the simplest way to solve the problem but maybe its incorrect because of "maximum product".

2. anonymous

ChatIndia, you cannot use x + 2x because that would imply they are the same number. It has to be x + 2y. I'm still working on this answer :p

3. anonymous

Yea because it says another number!

4. anonymous

nkili, in that case it would be very easy to solve. thanks for the hint

5. anonymous

i am sleepy,nkili will solve the problem. :)

6. anonymous

I'm really not sure about this one actually haha.... sorry :/

7. anonymous

proceed this way (x +2y)^2 = 144

8. anonymous

Does anyone disagree with 18?

9. anonymous

My answer key says that's the right answer, but how do you solve it.

10. anonymous

16

11. anonymous

Let x y = k y=k/x Then $\frac{k}{x}+2 x==12$ $\frac{k-12 x+2 x^2}{x}=0$ Derivative of the Numerator set to 0 then solved for x is x=3 $\left(\frac{k}{x}+2 x==12\text{/.}x\to 3\right) \text{is}\text{ }\left(6+\frac{k}{3}==12\right)$ k=18

12. anonymous

maxima minima trick :P

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