If 22 1/3% of a number n is 938, then n must be

Rationale

n must be 4,200.

To find the value of n, we set up the equation based on the percentage given: \( \frac{22}{3}\% \) of n equals 938. Converting the percentage to a decimal, we have \( \frac{22}{3} \times \frac{1}{100} \times n = 938 \). Solving this equation yields n = 4,200.

A (281,400) YOUR ANSWER

This choice is significantly larger than the calculated value of n. Since \( 22 \frac{1}{3}\% \) of 281,400 would result in a much higher number (over 62,000), it does not satisfy the condition that it equals 938.

B (42,000) YOUR ANSWER

Calculating \( 22 \frac{1}{3}\% \) of 42,000 results in 9,000, which is also far greater than 938. This choice does not align with the requirement of the problem and is therefore incorrect.

C (4,960) YOUR ANSWER

Taking \( 22 \frac{1}{3}\% \) of 4,960 gives approximately 1,107, which is again not equal to 938. Thus, this choice fails to meet the necessary condition outlined in the question.

D (4,200) CORRECT

This value is correct as it satisfies the equation \( \frac{22}{3}\% \) of 4,200, which equals 938. Thus, it is the only choice that meets the problem's requirements.

Conclusion

The correct calculation shows that n equals 4,200 when \( 22 \frac{1}{3}\% \) of n equals 938. The other choices either overshoot or undershoot this target, confirming that 4,200 is the only viable solution. This demonstrates the importance of understanding percentage calculations to solve for unknown values effectively.

If 22 1/3% of a number n is 938, then n must be

n must be 4,200.

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