If 8 : 4 :: 3.2 : x, what is the value of x?
1.6
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
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Set up the equation:
Using the values from the question, we write the proportion as an equation:
\( \frac{8}{4} = \frac{3.2}{x} \)
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Simplify the known ratio:
The ratio on the left side, \(8/4\), can be simplified:
\( \frac{8}{4} = 2 \)
So, the equation becomes:
\( 2 = \frac{3.2}{x} \)
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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 \(x\):
\( x = \frac{3.2}{2} \)
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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.
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