i am a 5 digit number greater than 60,000 but less than 70,000 my ones digit 1 less than my 10,000 digit all my other digits are the same the sum of my digit are 23. What is my number?
so it must start with a 6
6X,XXX
The unit digit can only be 5
so we have 6XXX5
then 6 + 3X+5 = 23
3x = 12
x = 4
your number is 64445
To find the 5-digit number that meets the given criteria (greater than 60,000, less than 70,000, ones digit is 1 less than the 10,000 digit, and the sum of the digits is 23), we can break down the problem step by step.
Step 1: Start with the range of numbers
We know the number is greater than 60,000 and less than 70,000. So, the range of numbers to consider is 60,000 to 69,999.
Step 2: Determine the condition for the ones digit
The ones digit is 1 less than the 10,000 digit. This means that the ones digit must be 1 less than a certain value, and this certain value must be the same as the other digits.
Step 3: Calculate the sum of the digits
The sum of all digits must add up to 23. This information will help us narrow down the possibilities.
Using this information, let's solve the problem:
1. Starting with the ones digit:
Since the ones digit is 1 less than the 10,000 digit, the only two possibilities for the ones digit are 0 or 9. However, the sum of the digits must be 23, so we eliminate 9 as an option because it would make the sum greater than 23. Therefore, the ones digit must be 0.
2. Moving to the 10,000 digit:
Since the ones digit is 0, and the sum of the digits is 23, we deduct 1 from the total sum to account for the missing 1 in the ones digit. This leaves us with a sum of 22 to distribute among the other digits.
3. Distributing the sum of 22:
To distribute the sum of 22 among the remaining four digits (which are the same), we divide 22 by 4, resulting in 5.5. However, since digits must be whole numbers, each of the four remaining digits must be either 5 or 6.
4. Analyzing possibilities:
Considering the options for the remaining four digits, we can list all possible combinations and check whether they fit the criteria:
a) All digits are 5: The sum of 5 + 5 + 5 + 5 + 0 = 20, which does not meet the condition of a sum equal to 23.
b) All digits are 6: The sum of 6 + 6 + 6 + 6 + 0 = 24, which does not meet the criteria either.
c) Three digits are 6, and one is 5: A sum of 5 + 6 + 6 + 6 + 0 = 23, which satisfies all the given conditions. Therefore, this is the correct combination.
Hence, the 5-digit number that fits the given criteria is 65,660.