Question

The sum of a number and twice another number is 12. What is their maximum product?

Answer 1

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".

Answer 2

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

Answer 3

Yea because it says another number!

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

Does anyone disagree with 18?

Answer 9

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

Answer 10

16

Answer 11

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

Answer 12

maxima minima trick :P