Ratio and proportion 0.1:10::x:400 =

Rationale

0.1:10 is equivalent to 4:400.

To solve the proportion 0.1:10::x:400, we can simplify the left side to find that 0.1 is 1/10 of 10, which corresponds to the same ratio as x being 1/100 of 400. Solving this gives x = 4.

A (25) YOUR ANSWER

If x were 25, the ratio would suggest that 0.1:10 is equivalent to 25:400. However, 25 is not 1/100 of 400; instead, it represents a much larger fraction of the second term, leading to an incorrect proportion.

B (5) YOUR ANSWER

Choosing x as 5 results in the ratio 0.1:10 being equivalent to 5:400. However, 5 is also not in the same proportion as 0.1 to 10, as it does not satisfy the relationship of being 1/100 of 400, thus making this choice incorrect.

C (50) YOUR ANSWER

If we set x as 50, the corresponding ratio would be 0.1:10 compared to 50:400. This indicates that 50 is not consistent with the original ratio, as it exceeds the expected proportion derived from the left side, confirming that this choice does not hold.

D (4) CORRECT

Setting x to 4 gives us the ratios 0.1:10 and 4:400, which simplifies correctly as both are 1:100. This confirms that 4 is indeed the correct value for x in maintaining the proportional relationship.

Conclusion

In solving the proportion 0.1:10::x:400, it is critical to find a value for x that maintains the same ratio. The successful calculation shows that x must equal 4 to preserve the ratio of 1/100, aligning with both sides of the proportion. Thus, 4 is the only answer that accurately reflects the relationship given in the question.

Ratio and proportion 0.1:10::x:400 =

0.1:10 is equivalent to 4:400.

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