Ratio and Proportion: 3 : 10 :: 12 : X

Rationale

X = 40

To solve the proportion 3 : 10 :: 12 : X, we can set up the equation 3/10 = 12/X and cross-multiply, resulting in 3X = 120. Dividing both sides by 3 gives us X = 40, confirming that this is the correct answer.

A (X = 3.6) YOUR ANSWER

This value does not satisfy the equation derived from the proportion. Substituting X = 3.6 into the equation 3/10 = 12/X results in an incorrect equality, indicating that this option fails to maintain the ratio.

B (X = 40) CORRECT

This is the correct answer, as substituting 40 back into the proportion yields the true statement 3/10 = 12/40. Both ratios simplify to 0.3, confirming the consistency of the proportion.

C (X = 0.27) YOUR ANSWER

Choosing X = 0.27 results in an invalid ratio when substituted into the proportion. The calculation 12/0.27 does not equal 10/3, thus failing to maintain the proportional relationship required.

D (X = 2.5) YOUR ANSWER

If we substitute X = 2.5 into the equation, we find that 12/2.5 does not equal 10/3. The resulting values do not match, which confirms that this choice does not fit the proportion.

Conclusion

The correct ratio in the proportion 3 : 10 :: 12 : X is established when X equals 40. This ensures that both sides of the proportion remain equivalent. The other options do not maintain this equality, rendering them incorrect and underscoring the importance of accurate calculations in solving ratio and proportion problems.

Ratio and Proportion: 3 : 10 :: 12 : X

X = 40

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