Three numbers are in the ratio of 5 : 3 : 7. The sum of their cubes is 61875. Find the three numbers.-Please explain.

Since the numbers are in the ratio of 5 : 3 : 7.
So suppose the numbers are 5x, 3x and 7x respectively.
Now according to the question we have;
$$\begin{gathered} {\left(5x\right)}^3+{\left(3x\right)}^3+{\left(7x\right)}^3 = 61875 \\ \Rightarrow 125x^3+27x^3+343x^3 = 61875 \\ \Rightarrow 495x^3 = 61875 \\ \Rightarrow x^3 = \frac{61875}{495} \\ \Rightarrow x = \sqrt[3]{\frac{61875}{495}} = \sqrt[3]{125} \\ \Rightarrow x = 5 \end{gathered}$$
Therefore the numbers are $5x \mathrm{i}.\mathrm{e}. 5\times 5 = 25; 3x \mathrm{i}.\mathrm{e}. 3\times 5 = 15; 7x \mathrm{i}.\mathrm{e}. 7\times 5 = 35$