If 5 is to 30 as X is to 1, find the value of X. (Round to the nearest tenth.)

Rationale

X equals 6.

To find the value of X, we need to recognize the relationship in the proportion given. The ratio of 5 to 30 is the same as the ratio of X to 1, and solving the equation shows that X must be 6 to maintain this relationship.

A (6) CORRECT

This choice correctly represents the solution to the proportion. The relationship can be expressed as \( \frac{5}{30} = \frac{X}{1} \). Simplifying \( \frac{5}{30} \) gives \( \frac{1}{6} \), leading to \( X = 6 \) when cross-multiplying.

B (5.5) YOUR ANSWER

This option does not satisfy the proportional relationship established by the problem. If we substitute 5.5 into the equation \( \frac{5}{30} = \frac{5.5}{1} \), we find that \( \frac{5.5}{1} \) simplifies to 5.5, which does not equal \( \frac{1}{6} \). Thus, it is incorrect.

C (5) YOUR ANSWER

Choosing 5 fails to maintain the ratio between the numbers. If we set \( \frac{5}{30} = \frac{5}{1} \), we see that it simplifies to \( \frac{1}{6} \) on the left side and 5 on the right side, which are clearly not equal. Therefore, this choice is not valid.

D (4.5) YOUR ANSWER

This choice also does not fulfill the original proportion. Substituting 4.5 results in \( \frac{5}{30} = \frac{4.5}{1} \), which simplifies to \( \frac{1}{6} \) on the left and 4.5 on the right. Since these values differ, this option is incorrect.

Conclusion

The proportional relationship in the question requires that the value of X matches the established ratio of 5 to 30. Through solving the proportion, we find that X must equal 6 to maintain this equality, while all other choices lead to incorrect interpretations of the ratio. Understanding these relationships is essential in solving similar proportional problems effectively.

If 5 is to 30 as X is to 1, find the value of X. (Round to the nearest tenth.)

X equals 6.

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