Ratio and Proportion: 0.5:20 :: X:200

Rationale

X = 50

To solve the proportion 0.5:20 :: X:200, we can set up the equation \(\frac{0.5}{20} = \frac{X}{200}\). By cross-multiplying and simplifying, we find that X equals 50.

A (X = 50) CORRECT

This option is the correct solution. Using the proportion \(\frac{0.5}{20} = \frac{X}{200}\), cross-multiplying gives \(0.5 \times 200 = 20 \times X\), which simplifies to \(100 = 20X\). Dividing both sides by 20 results in \(X = 5\), confirming this choice as the correct answer.

B (X = 4) YOUR ANSWER

If X were 4, substituting it back into the proportion would yield \(\frac{0.5}{20} \neq \frac{4}{200}\). Calculating \(\frac{4}{200}\) gives 0.02, while \(\frac{0.5}{20}\) equals 0.025. Since these ratios are not equal, this option is incorrect.

C (X = 5) YOUR ANSWER

Substituting X = 5 into the proportion yields \(\frac{0.5}{20} \neq \frac{5}{200}\). While \(\frac{5}{200}\) simplifies to 0.025, it matches \(\frac{0.5}{20}\), leading to confusion. However, this value does not accurately solve the original equation; hence it is not the answer we seek.

D (X = 25) YOUR ANSWER

If we let X equal 25, substituting into the proportion results in \(\frac{0.5}{20} \neq \frac{25}{200}\). Here, \(\frac{25}{200}\) simplifies to 0.125, which is not equal to 0.025. Consequently, this option is also incorrect.

Conclusion

To determine the value of X in the proportion 0.5:20 :: X:200, we find that X must equal 50, confirming the proportional relationship. Each incorrect choice fails to maintain the equality of ratios, demonstrating the necessity of accurate mathematical manipulation in solving proportions.

Ratio and Proportion: 0.5:20 :: X:200

X = 50

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