I am a five digit number greater than 60,000 but less than 70,000.my ones digit is 1 less than my ten thousands digit.all my other digits are the same.the sum of my digits is 23.what am i
Clearly, the number must look like this:
6X,XX5
Also 3X + 11 = 23
continue ....
To find the five-digit number that meets these conditions, we can proceed step by step:
Step 1: Identify the criteria given:
- The number is greater than 60,000 and less than 70,000.
- The ones digit is 1 less than the ten-thousands digit.
- All other digits are the same.
- The sum of the digits is 23.
Step 2: Let's start by considering the ten-thousands digit. Since all the other digits are the same, we need to find a digit that gives us a sum of 23 when repeated four times (since there are four other digits).
Step 3: We know that the sum of the digits is 23, and each digit (except for the ten-thousands digit) is the same. If we divide 23 by 4, we get a quotient of 5 with a remainder of 3. This tells us that four identical digits sum up to 20, and we have an additional digit with a value of 3 left.
Step 4: Since the ones digit is 1 less than the ten-thousands digit, and all other digits are the same, we can pair up the remaining value (3) with the ten-thousands digit (X) and increase X by 1. This gives us a value of 3 for the ones digit.
Step 5: Based on the information gathered, we can form the number: XYYYY.
- The ten-thousands digit is X.
- The ones digit is 3.
- All other digits are Y.
Now, we need to find the value of Y.
Step 6: The sum of all the digits is 23. Since the ten-thousands digit is X, the sum of the other three Y digits is 23 - X - 3 = 20 - X.
Step 7: From Step 3, we learned that four identical digits sum up to 20. Therefore, Y = (20 - X)/3.
Step 8: Since all digits must be integers, we need to find a value of X that makes Y an integer. We can try different values for X to find a solution.
If we substitute X = 1 into the equation Y = (20 - X)/3, we get Y = (20 - 1)/3 = 19/3. Since Y is not an integer, X = 1 does not satisfy the conditions.
If we substitute X = 2 into the equation Y = (20 - X)/3, we get Y = (20 - 2)/3 = 18/3 = 6. This value of Y is an integer.
Step 9: We have found that X = 2 and Y = 6. Therefore, the number that satisfies the given conditions is 26YYY.
Step 10: To check if this number is within the range of 60,000 to 70,000, we can substitute different values for Y and see if the resulting number falls within the range.
If Y = 0, the number would be 26000 which is within the given range.
Therefore, the five-digit number that satisfies all the conditions is 26000.