Ratio and Proportion: 9 : X :: 5 : 300 (Enter numeric value only.)

Rationale

9 : X :: 5 : 300 implies that X equals 540.

To solve the ratio, we can set up the proportion using cross-multiplication. By equating the products of the means and extremes, we find that \(9 \times 300 = 5 \times X\), leading to the correct value of \(X\) as 540.

A (450) YOUR ANSWER

To check this choice, we substitute \(X = 450\) into the equation \(9 : 450\) and \(5 : 300\). This gives us \(9 \times 300 = 2700\) and \(5 \times 450 = 2250\). Since these values do not match, 450 is not a correct answer.

B (540) CORRECT

This choice correctly maintains the ratio. By substituting \(X = 540\), we calculate \(9 : 540\) and \(5 : 300\), confirming that \(9 \times 300 = 2700\) and \(5 \times 540 = 2700\). Thus, both sides of the proportion are equal, making 540 the correct answer.

C (600) YOUR ANSWER

If we substitute \(X = 600\), we compute \(9 : 600\) compared to \(5 : 300\). The calculations yield \(9 \times 300 = 2700\) and \(5 \times 600 = 3000\). These results do not equate, indicating that 600 is not the correct value for \(X\).

D (480) YOUR ANSWER

Testing this option with \(X = 480\) leads to \(9 : 480\) and \(5 : 300\). The calculations show \(9 \times 300 = 2700\) and \(5 \times 480 = 2400\). As these products are not equal, 480 is also an incorrect answer.

Conclusion

The solution to the proportion 9 : X :: 5 : 300 reveals that \(X\) must equal 540 to maintain the equality of the ratios. The method of cross-multiplication effectively demonstrates that only option B satisfies the conditions of the proportion, while the other choices yield unequal products, confirming them as incorrect.

Ratio and Proportion: 9 : X :: 5 : 300 (Enter numeric value only.)

9 : X :: 5 : 300 implies that X equals 540.

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