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Three numbers are to one another 2:3:4. The sum of their cubes is 0.334125. Find the numbers.

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Lest assume the numbers be 2a, 3a, and 4a.

 According to the question: 

(2a)3+ (3a)3+(4a)3 = 0.334125 

= 8a3+27 a3+64 a3 = 0.334125 

=99 a3 = 0.334125

= a3 = \(\frac{334125}{1000000\times99} = \frac{3375}{1000000}\)

= a = \(\frac{\sqrt[3]{3375}}{1000000}\)

= a = \(\frac{\sqrt[3]{3375}}{\sqrt[3]{1000000}}\)

= a = \(\frac{15}{100} = 0.15\)

Thus the numbers are:

2×0.15 = 0.30 

3×0.15 = 0.45 

4×0.15 = 0.60

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