Question

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

Answer 1

Let the numbers be 2x, 3x and 4x.

According to the question:​

$$\begin{gathered} {\left(2x\right)}^3+{\left(3x\right)}^3+{\left(4x\right)}^3=0.334125 \\ \Rightarrow 8x^3+27x^3+64x^3=0.334125 \\ \Rightarrow 8x^3+27x^3+64x^3=0.334125 \\ \Rightarrow 99x^3=0.334125 \\ \Rightarrow x^3=\frac{{\cancel{334125}}^{3375}}{1000000\times \cancel{99}} \\ \Rightarrow x=\sqrt[3]{\frac{3375}{1000000}} \\ \Rightarrow x=\frac{\sqrt[3]{3375}}{\sqrt[3]{1000000}} \\ \Rightarrow x=\frac{15}{100}=0.15. \end{gathered}$$

Thus, the numbers are:

$$\begin{gathered} 2\times 0.15=0.30 \\ 3\times 0.15=0.45 \\ 4\times 0.15=0.60 \end{gathered}$$