i am a 4 digit number.my thousands didgit is 4 less than my tens digit.my hundreds digit equals the sum of my tens digit and my ones digit.my tens digit is 4 more than my ones digit.my ones digit is 1.what number am i?
Ones digit = 1.
Tens digit = 4 + 1 = 5.
Hundreds digit = 5 + 1 = 6.
Thousands digit is= 5 - 4 = 1.
The # is 1651.
To find the number that satisfies the given conditions, let's break down the problem step-by-step.
1. Start with the clue: "I am a 4-digit number."
Since the problem states that the number is 4 digits, we know that the number is greater than or equal to 1000 and less than 10000.
2. "My thousands digit is 4 less than my tens digit."
The thousands digit is 4 less than the tens digit. This means that the thousands digit must be smaller than the tens digit by 4. Since the ones digit is given as 1, we can start by checking values for the thousands and tens digits.
Let's go through all possible values for these digits:
- Thousands digit: 2 (6 less than tens digit)
- Tens digit: 6 (4 more than ones digit)
- Ones digit: 1 (given)
Now let's check if the conditions for the hundreds digit are met.
3. "My hundreds digit equals the sum of my tens digit and my ones digit."
The hundreds digit is equal to the sum of the tens and ones digits. In our assumed values:
- Tens digit: 6
- Ones digit: 1
- Hundreds digit: 6 + 1 = 7
The sum of the tens and ones digits is 7, which matches the hundreds digit.
4. To determine the thousands digit, we recall that it is 4 less than the tens digit. In our assumed values:
- Tens digit: 6
- Thousands digit: 6 - 4 = 2
The thousands digit is indeed 2, which satisfies the condition.
5. Now we have our 4-digit number:
Thousands digit: 2
Hundreds digit: 7
Tens digit: 6
Ones digit: 1
Therefore, the number that satisfies all the given conditions is 2,761.