Solving Proportion 8 : 4 :: 3.2 : x - Find the Value of x

This question involves solving a proportion, which is a statement that two ratios are equal. The given proportion is:

\(8 : 4 :: 3.2 : x\)

This can be read as "8 is to 4 as 3.2 is to x".

Understanding Proportions

A proportion sets two ratios equal to each other. Mathematically, if we have a proportion like \(a : b :: c : d\), it can be written as a fraction:

\( \frac{a}{b} = \frac{c}{d} \)

In our case, \(a = 8\), \(b = 4\), \(c = 3.2\), and \(d = x\).

Step-by-Step Calculation

1. Set up the equation:

   Using the values from the question, we write the proportion as an equation:

   \( \frac{8}{4} = \frac{3.2}{x} \)

2. Simplify the known ratio:

   The ratio on the left side, \(8/4\), can be simplified:

   \( \frac{8}{4} = 2 \)

   So, the equation becomes:

   \( 2 = \frac{3.2}{x} \)

3. Solve for x:

   To find the value of \(x\), we can rearrange the equation. Multiply both sides by \(x\):

   \( 2 \times x = 3.2 \)

   \( 2x = 3.2 \)

   Now, divide both sides by 2 to isolate \(x\):

   \( x = \frac{3.2}{2} \)

4. Calculate the final value:

   Performing the division:

   \( x = 1.6 \)

Conclusion

By setting up the proportion and solving the equation step-by-step, we find that the value of \(x\) is 1.6.