Question

The ratio x:8 is equivalent to the ratio 27:x^2. What is the value of x?

Answer 1

We are given that the following ratios are equivalent:

$\begin{gathered} x\colon8 \\ 27\colon x^2 \end{gathered}$

This means that the following relationship holds:

$\frac{x}{8}=\frac{27}{x^2}$

Now, to solve for "x" we can cross multiply the equation:

$x\times x^2=27\times8$

Solving the operations:

$x^3=216$

Now we take the cubic root to both sides:

$x=\sqrt[3]{216}$

Solving the operation:

$x=6$

Therefore, the value of "x" is 6.