Let x > 0, y > 0, and z > 0. If (1/x : 1/y : 1/z) = 2 : 5 : 9, then which of the following is equivalent to x:y:z?

Rationale

x:y:z = 1:2.5:4.5.

To solve the ratio (1/x : 1/y : 1/z) = 2 : 5 : 9, we can first express this in terms of x, y, and z. By taking the reciprocal of the ratio components, we find that x:y:z is equivalent to the ratio of the inverse values, which simplifies to 1:2.5:4.5. This can be further reduced to a more usable form.

A (10:18:45) YOUR ANSWER

This ratio does not maintain the proportional relationships established by the initial ratios. When simplified, the values do not correspond to the calculated equivalent of 1:2.5:4.5.

B (14:10:45) YOUR ANSWER

Similar to option A, the ratio of 14:10:45 does not simplify correctly to match the required proportion of 1:2.5:4.5, indicating it is not equivalent to the properly derived ratio.

C (18:10:35) YOUR ANSWER

This option fails to satisfy the derived ratio as well. Upon simplification, it does not maintain the same comparative proportions as that of 1:2.5:4.5.

D (35:14:10) YOUR ANSWER

The ratio 35:14:10 also does not align with the derived proportions from the initial equation. It simplifies incorrectly and does not reflect the necessary relationship between x, y, and z.

E (1.887615741) CORRECT

This is a numerical value that cannot be directly equated to the ratios of x, y, and z. It appears to be a decimal representation rather than a ratio format and does not correspond to the derived ratio of 1:2.5:4.5.

Conclusion

The relationship established by (1/x : 1/y : 1/z) = 2 : 5 : 9 simplifies to x:y:z = 1:2.5:4.5, which is not represented accurately in any of the provided choices. Each option fails to reflect the correct proportional relationship. Thus, the correct equivalent ratio is derived from the initial setup but is not explicitly listed among the answer choices.

Let x > 0, y > 0, and z > 0. If (1/x : 1/y : 1/z) = 2 : 5 : 9, then which of the following is equivalent to x:y:z?

x:y:z = 1:2.5:4.5.

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