Certainly! Let's solve this problem step-by-step.
We are given that the ratio [tex]\( x : 50 \)[/tex] is equivalent to the ratio [tex]\( 8 : x \)[/tex]. This can be written mathematically as:
[tex]\[
\frac{x}{50} = \frac{8}{x}
\][/tex]
To solve for [tex]\( x \)[/tex], we can use cross-multiplication. Cross-multiplying the two fractions gives us:
[tex]\[
x \cdot x = 8 \cdot 50
\][/tex]
Simplifying the right side, we get:
[tex]\[
x^2 = 400
\][/tex]
To find the value of [tex]\( x \)[/tex], we take the square root of both sides of the equation:
[tex]\[
x = \sqrt{400}
\][/tex]
The positive square root of 400 is:
[tex]\[
x = 20
\][/tex]
Therefore, the positive value of [tex]\( x \)[/tex] that satisfies the condition [tex]\( x : 50 \)[/tex] being equivalent to [tex]\( 8 : x \)[/tex] is:
[tex]\[
\boxed{20}
\][/tex]
