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

Rationale

x = 4.

To solve the proportion 0.1:10::x:400, we can use cross-multiplication. This method reveals that x is equal to 4 when the proportion is maintained, ensuring that the ratios are equivalent.

A (5) YOUR ANSWER

If x were 5, the ratio would be 0.1:10::5:400. Cross-multiplying gives 0.1 * 400 = 40 and 10 * 5 = 50, which are not equal. Thus, 5 does not satisfy the proportion.

B (4) CORRECT

Using x = 4, we have 0.1:10::4:400. Cross-multiplying yields 0.1 * 400 = 40 and 10 * 4 = 40, confirming that both sides are equal. Therefore, 4 maintains the proportional relationship.

C (25) YOUR ANSWER

If x equals 25, the ratio becomes 0.1:10::25:400. Cross-multiplying results in 0.1 * 400 = 40, while 10 * 25 = 250, which are not equal. Hence, 25 is not a valid solution.

D (50) YOUR ANSWER

Assuming x is 50, the proportion would be 0.1:10::50:400. Cross-multiplying gives 0.1 * 400 = 40, and 10 * 50 = 500, which are unequal. Therefore, 50 does not satisfy the proportion.

Conclusion

The solution to the proportion 0.1:10::x:400 is x = 4, as validated by cross-multiplication confirming equality on both sides of the ratio. The other options—5, 25, and 50—fail to preserve the proportional relationship, demonstrating that only 4 correctly balances the equation.

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

x = 4.

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