Let's analyze the problem.

The key information is:

• Mya rounds the mystery number to the nearest ten and gets 400.
• Sophia rounds the same mystery number to the nearest hundred and gets 400.

Step 1: Rounding to the nearest hundred

For the number to round to 400 when rounded to the nearest hundred, the number must be between 350 and 449 (since any number from 350 to 449 rounds to 400).

Step 2: Rounding to the nearest ten

For the number to round to 400 when rounded to the nearest ten, the number must be between 395 and 404 (since any number from 395 to 404 rounds to 400 when rounded to the nearest ten).

Step 3: Intersection of these ranges

• From rounding to the nearest hundred, the number must be between 350 and 449.
• From rounding to the nearest ten, the number must be between 395 and 404.

Thus, the mystery number must be within the intersection of these two ranges, which is 395 to 404.

Step 4: Evaluating the answer choices

Now let's check the options:

• A: 393 → Does not fit the range.
• B: 399 → Fits the range.
• C: 403 → Fits the range.
• D: 406 → Does not fit the range.
• E: 394 → Does not fit the range.

Conclusion:

The possible numbers that fit are B (399) and C (403).

Would you like further details, or do you have any questions?

Related Questions:

1. What happens when rounding numbers ending in 5?
2. Can a number be rounded differently to the nearest ten and hundred?
3. How do rounding rules differ between different bases?
4. What is the smallest number that rounds to 500 when rounded to the nearest hundred?
5. How can I determine rounding behavior for decimals?

Tip:

When rounding, always remember to check both lower and upper boundaries for the range where the number could lie.