Ratio and Proportion: 4:10 :: 5:X

Rationale

X = 12.5

To solve for X in the proportion 4:10 :: 5:X, we can set up the equation 4/10 = 5/X and cross-multiply, leading to the conclusion that X equals 12.5.

A (X = 10.5) YOUR ANSWER

This choice is incorrect because substituting X with 10.5 does not maintain the equality of the original ratio. Using 4:10 and 5:10.5 results in a ratio of 5/10.5, which simplifies to approximately 0.476, differing from the ratio of 0.4 established by 4:10.

B (X = 20) YOUR ANSWER

If X were equal to 20, the new ratio would be 5:20, which simplifies to 1:4, a value of 0.25. This does not match the ratio of 4:10, which is 0.4. Thus, this choice fails to satisfy the proportion.

C (X = 12.5) CORRECT

This is the correct choice. When X is 12.5, the ratio 5:X becomes 5:12.5, which simplifies to 1:2.5 or 0.4, matching the ratio of 4:10. Therefore, this choice correctly maintains the equality in the proportion.

D (X = 25) YOUR ANSWER

Choosing X as 25 gives the new ratio of 5:25, simplifying to 1:5 or 0.2. This is far from the original ratio of 4:10, which is 0.4, making this option incorrect.

Conclusion

In the proportion 4:10 :: 5:X, the correct value for X that preserves the equality of the ratios is 12.5. The other choices either produce ratios that differ from the original or do not satisfy the proportional relationship required by the question. Thus, understanding how to manipulate ratios and proportions is crucial for solving such problems accurately.

Ratio and Proportion: 4:10 :: 5:X

X = 12.5

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