Ratio and Proportion: 3:5 :: X:10

Rationale

X = 6

To maintain the ratio of 3:5 when the second term is 10, the first term, represented by X, must equal 6. This is derived from the properties of equivalent ratios, where the two ratios can be cross-multiplied to find the unknown value.

A (X = 10) YOUR ANSWER

If X were 10, the ratio would be 10:10, which simplifies to 1:1, deviating from the original ratio of 3:5. This choice does not maintain the proportional relationship required by the question, as it creates an entirely different ratio.

B (X = 6) CORRECT

This choice correctly maintains the ratio 3:5 when paired with 10. By setting up the proportion 3/5 = X/10 and cross-multiplying, we find that 3 * 10 = 5 * X, leading to X = 6. Thus, this is the correct solution.

C (X = 3) YOUR ANSWER

If X were 3, then the ratio would be 3:10. This does not match the original ratio of 3:5, as 3:10 simplifies to a different proportion altogether. Therefore, this choice fails to satisfy the conditions set by the problem.

D (X = 8) YOUR ANSWER

With X set to 8, the resulting ratio would be 8:10, which simplifies to 4:5. This also does not correspond to the original ratio of 3:5, indicating that this choice does not uphold the proportional relationship required.

Conclusion

The relationship of ratios necessitates that equivalent fractions maintain their proportional integrity. In this case, X must equal 6 to uphold the ratio of 3:5 when the second term is 10. All other options either create different ratios or fail to satisfy the original proportional condition, reinforcing the correctness of the choice X = 6.

Ratio and Proportion: 3:5 :: X:10

X = 6

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