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Tough ratio problem

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by just4myself » Mon Aug 25, 2008 9:09 am
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 cartoon?

1) x^1/3
2) (2x/3)^1/3
3) (3x/2)^1/3
4) 2/3* (x)^1/3
5) 3/2* (x)^1/3

Thank you...
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by kris610 » Mon Aug 25, 2008 9:59 am
I would go with B. From the given data, if you assume 3a as the length, you have the volume as 12*(a^3) = x. From this find a in terms of x, and find the required height, which is 2a.
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by just4myself » Mon Aug 25, 2008 10:27 am
B is the right ans....Thanks
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by jeffxujian » Mon Aug 25, 2008 1:18 pm
IMO C
here is how I tackle it, maybe easier for you

the ratio is 3:2:2, so assume the actual break down is 6, 4, 4, thus X is 96
then since the power all the same, all you need to find is the base equal to 64, because 64^1/3=4. B is the one!

Jeff
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by jeffxujian » Mon Aug 25, 2008 1:19 pm
typo I meant B
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