a number rounds off to 4000.the digits in the hundreds place is twice the digits in the tens place.the sum of the digits is 12.the number uses only two different digits.find the number
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To find the number based on the given information, we need to follow a systematic approach. Let's break down the problem step by step:
Step 1: Identify the key information provided in the problem:
- The number rounds off to 4000.
- The digit in the hundreds place is twice the digit in the tens place.
- The sum of the digits is 12.
- The number uses only two different digits.
Step 2: Determine the digit in the hundreds place:
Since the number rounds off to 4000, we know that the digit in the thousands place is 4. Therefore, the digit in the hundreds place must be either 3 or 4, as the number uses only two different digits.
Step 3: Determine the digit in the tens place:
The sum of the digits is stated to be 12, which means that the remaining three digits (thousands, hundreds, and units) must add up to 12. Since one digit is already 4, the remaining two digits must add up to 8. We can try different values for the tens place until we find the one that satisfies the condition.
Let's start by assuming that the tens place is 1. In this case, the units place needs to be 7 (since 4 + 3 + 1 + 7 = 12), but this number does not round off to 4000.
Let's try another value for the tens place, assuming it's 2. In this case, the units place would need to be 6 (since 4 + 3 + 2 + 6 = 15), but this number does not satisfy the condition either.
Finally, let's assume that the tens place is 3. In this case, the units place must be 5 (since 4 + 3 + 3 + 5 = 15). Now, we have found a solution that satisfies all the given conditions.
Therefore, the number is 4355.