What is the value of x in the expression 8:x::16:8?

To find the value of x in the proportion 8:x::16:8, we can set it up as a cross-multiplication problem. This ratio indicates that 8 is to x as 16 is to 8. Therefore, we can express this relationship mathematically as:

8 * 8 = 16 * x.

Calculating the left side gives us:

64 = 16 * x.

Next, we solve for x by dividing both sides of the equation by 16:

x = 64 / 16.

Performing the division, we find that:

x = 4.

This solution demonstrates the principles of ratios and how to manipulate them to find unknown values. Understanding ratios and proportions is a fundamental skill in various applications, including power engineering, where balancing values and measuring relationships is often necessary.