Final answer:
The digit 'A' in the numeral 3AA1 that makes it divisible by 9 is 7. This is determined by the rule that the sum of the digits of the number must be divisible by 9, and through the calculation, we find that both A's must sum to 14, meaning each A is equal to 7.
Step-by-step explanation:
The four-digit numeral 3AA1 is divisible by 9. To find the digit represented by A, we know that the sum of the digits in the number must be divisible by 9. Here's the step-by-step explanation:
- Let A represent the unknown digit.
- The sum of the digits in the number 3AA1 would be 3 + A + A + 1.
- Combine like terms to simplify the expression: 4 + 2A.
- Since the sum must be divisible by 9, let us find the multiple of 9 that is just greater than 4, which is 9 itself.
- Set up the equation 4 + 2A = 9 to find the value of A.
- Solving the equation: 2A = 9 - 4, which simplifies to 2A = 5.
- Dividing both sides by 2 gives us A = 2.5. Since A must be a whole digit, it can't be 2.5, so we must try the next multiple of 9, which is 18.
- We now solve 4 + 2A = 18, which simplifies to 2A = 14. Dividing by 2, we find A = 7.
Therefore, the digit A must represent the number 7 to make the numeral divisible by 9.