Problem Solving

The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3:2:2. In terms of x, which of the following equals the height of the carton, in feet?

A.3√x
B.3√[(2x)/3]
C.3√[(3x)/2]
D.(2/3) 3√x
E.(3/2) 3√x

OAB


I have solved till - k = 3√x/12.

Now what will be the next?

Please advise..

Thanks

rsarashi wrote:The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3:2:2. In terms of x, which of the following equals the height of the carton, in feet?

A.3√x
B.3√[(2x)/3]
C.3√[(3x)/2]
D.(2/3) 3√x
E.(3/2) 3√x

OAB


I have solved till - k = 3√x/12.

Now what will be the next?

Please advise..

Thanks

Since the height is 2k, you just multiply your number by 2, and work your way to the correct answer.

I did it below, so if you want to do it own your own, don't look at what I did until you after you do it yourself.

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[spoiler]2 * ∛(x/12) = ∛(2³x/12) = ∛(2x/3)[/spoiler]

The correct answer is B.

rsarashi wrote:The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3:2:2. In terms of x, which of the following equals the height of the carton, in feet?

A.∛x
B.∛[(2x)/3]
C.∛[(3x)/2]
D.(2/3) ∛x
E.(3/2) ∛x

OAB


Thanks

You can also just pick easy numbers.

Length: 3
Width: 2
Height: 2

x = 2 * 2 * 3 = 12

When x = 12, the height is 2. No just plug and chug with the answers, inserting 12 for x, until one of them spits out a height of 2.

A.∛x = ∛12 --> not 2

B.∛[(2x)/3] --> ∛(2*12/3) --> ∛8 = 2. And we're done. B is the answer.

(And in the future, please be careful about formatting. I initially read ∛ as 3 * √, and I'd imagine I'm not the only one who misinterpreted this way. )