Iam a 4 digit number. iam less than 5000 my hundreds digit is double my unit my tens digit is half of my unit digit. my thousand digit is the same as my unit digit. what number am I
The number must be of the form
2xx2
or
4xx4
since the units digit must be even (tens is half of units)
So that makes it easy to fill in the x's.
To find the number, we need to analyze the given information step by step.
1. "I am a 4-digit number": This tells us that the number is composed of four digits.
2. "I am less than 5000": This means the number is less than 5000.
Now let's break down the given information to determine the value of each digit:
3. "My hundreds digit is double my unit": This means that the hundreds digit is twice the value of the unit digit.
4. "My tens digit is half of my unit digit": This indicates that the tens digit is half the value of the unit digit.
5. "My thousand digit is the same as my unit digit": This suggests that the thousand digit is equal to the unit digit.
Based on the information provided, we can conclude that the unit digit, tens digit, and thousand digit are the same. Let's represent the unit digit as "x", so the tens digit is "x/2", and the hundreds digit is "2x".
Now, we need to find a suitable value for "x" that satisfies all the conditions.
Since the thousands digit is also equal to the unit digit, this means that the thousands digit is "x" as well.
To form the 4-digit number, we can write it as "2x(x/2)x".
For example, if we let "x" be 2, the number becomes 2,242. However, we need to check if this number satisfies the given conditions.
The number is less than 5000, so 2,242 is a valid option. However, there might be other possibilities as well.
By systematically substituting different values of "x" and checking if the given conditions hold, we can find the final answer.
Alternatively, we can use a programming language or a spreadsheet program to automate the process and quickly find the answer.
By iterating through the possible values of "x" (0 to 9) and checking the conditions, we can find that the correct number is 2128.
Therefore, the answer is 2128.