In the ratio 0.5 : 20 :: X : 200, what is X?

Rationale

X equals 5 in the ratio 0.5 : 20 :: X : 200.

To find the value of X that maintains the same ratio, we can set up a proportion: \( \frac{0.5}{20} = \frac{X}{200} \). Solving for X yields 5, ensuring the ratios are equivalent.

A (2) YOUR ANSWER

If X were 2, the ratio would be \( \frac{0.5}{20} = \frac{2}{200} \). Simplifying \( \frac{2}{200} \) gives \( \frac{1}{100} \), which is not equal to \( \frac{0.5}{20} \) or \( \frac{1}{40} \). Thus, this choice does not maintain the required ratio.

B (5) CORRECT

When X is 5, we have \( \frac{0.5}{20} = \frac{5}{200} \). Simplifying both sides gives \( \frac{1}{40} \) on the left and \( \frac{1}{40} \) on the right, confirming that this choice maintains the correct ratio.

C (10) YOUR ANSWER

If X is 10, the ratio becomes \( \frac{0.5}{20} = \frac{10}{200} \). Simplifying \( \frac{10}{200} \) results in \( \frac{1}{20} \), which does not equal \( \frac{0.5}{20} \) or \( \frac{1}{40} \). Hence, this choice does not satisfy the proportion.

D (15) YOUR ANSWER

With X as 15, the equation forms \( \frac{0.5}{20} = \frac{15}{200} \). Simplifying \( \frac{15}{200} \) results in \( \frac{3}{40} \), which is again not equal to \( \frac{0.5}{20} \) or \( \frac{1}{40} \). Therefore, this choice also fails to maintain the ratio.

Conclusion

In solving the proportion \( 0.5 : 20 :: X : 200 \), X must be 5 to preserve the equality of the ratios. The other choices do not satisfy the condition set by the original ratio, making them incorrect. This demonstrates the importance of maintaining consistent ratios when solving for unknown values in proportional relationships.

In the ratio 0.5 : 20 :: X : 200, what is X?

X equals 5 in the ratio 0.5 : 20 :: X : 200.

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