Solve for x: 3:2 :: 24:x

Rationale

16 is the correct value for x in the proportion 3:2 :: 24:x.

To solve the proportion, we can set up the equation 3/2 = 24/x. Cross-multiplying gives us 3x = 48, leading to x = 16.

A (16) CORRECT

This choice is correct. By cross-multiplying the proportion 3:2 = 24:x, we find that 3x = 48, resulting in x = 16. This confirms that 16 maintains the same ratio as 3:2 when compared to 24.

B (12) YOUR ANSWER

Choosing 12 would result in the proportion 3:2 = 24:12, which simplifies to 3/2 = 2. This is incorrect, as 2 does not equal 1.5, indicating that 12 does not maintain the same ratio as required.

C (2) YOUR ANSWER

If we substitute 2 into the proportion, we get 3:2 = 24:2. This simplifies to 3/2 = 12, which is also incorrect because 12 does not equal 1.5. Thus, 2 fails to satisfy the proportion.

D (22) YOUR ANSWER

Using 22 in the proportion gives us 3:2 = 24:22, which simplifies to 3/2 = 1.0909. This does not match the original ratio of 1.5, demonstrating that 22 is not a valid solution.

Conclusion

In solving the proportion 3:2 :: 24:x, we determine that x must equal 16 to maintain the correct ratios. The other options fail to satisfy the relationship established by the initial values, illustrating the importance of proper ratio preservation in mathematical proportions.

Solve for x: 3:2 :: 24:x

16 is the correct value for x in the proportion 3:2 :: 24:x.

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