i am an odd number between 300 and 400.none of my digits are the same.the sum of the digits is five times my hundreds digit.
you know it must look like
3xy
also 3+x+y = 5x
y = 4x - 3
if x = 1, y = 1 , number is 311 , but none are the same
if x = 2, y = 5, number is 325 , looks ok
if x = 3, y = 9 , number is 339, but none can be the same
if x = 4, y = 13, not possible
the number is 325
Let's break down the information given:
1. You are an odd number between 300 and 400.
2. None of your digits are the same.
3. The sum of the digits is five times your hundreds digit.
Let's use these clues to find the number step by step:
Step 1: The number must be odd, so the ones digit can only be 1, 3, 5, 7, or 9.
Step 2: None of the digits are the same, so we can eliminate any numbers with repeated digits. This means the ones digit cannot be 1, 3, or 5, as they are already used in the hundreds and tens digits.
Step 3: Since the sum of the digits is five times the hundreds digit, let's examine the range of possibilities for the hundreds digit. From 300 to 400, the possible hundreds digits are 3, 4, and 6.
Step 4: Let's consider each possibility for the hundreds digit:
- If the hundreds digit is 3, then the tens and ones digits must add up to 15 (since 3 * 5 = 15). However, none of the remaining numbers (7, 8, and 9) sum to 15, so 3 cannot be the hundreds digit.
- If the hundreds digit is 4, then the tens and ones digits must add up to 20 (since 4 * 5 = 20). The remaining numbers (6, 7, and 9) can be used to create a sum of 20 (6 + 9 + 5), so 4 can be the hundreds digit.
Therefore, the number you are is 469.
To find the odd number that meets the given conditions, let's break down the information provided step by step:
1. Start with the range: The number is between 300 and 400, so it falls in the range of 301 to 399.
2. The number is an odd number: An odd number is not divisible by 2, so all possible numbers in the given range can be considered.
3. None of the digits are the same: This means that the hundreds, tens, and units digits are all different.
4. The sum of the digits is five times the hundreds digit: Let's represent the hundreds digit as "H", the tens digit as "T", and the units digit as "U". Based on this information, we have the equation H + T + U = 5H.
Now, let's go through the possible numbers in the range and check if they meet all the conditions:
For 301:
H = 3, T = 0, U = 1
3 + 0 + 1 = 5(3) -> 4 = 15 (Not correct)
For 302:
H = 3, T = 0, U = 2
3 + 0 + 2 = 5(3) -> 5 = 15 (Not correct)
For 303:
H = 3, T = 0, U = 3
3 + 0 + 3 = 5(3) -> 6 = 15 (Not correct)
Continue this process until we find the number that satisfies all the conditions:
For 398:
H = 3, T = 9, U = 8
3 + 9 + 8 = 5(3) -> 20 = 15 (Not correct)
For 399:
H = 3, T = 9, U = 9
3 + 9 + 9 = 5(3) -> 21 = 15 (Not correct)
None of the numbers in the range satisfy all the conditions. Therefore, there is no odd number between 300 and 400 where none of the digits are the same, and the sum of the digits is five times the hundreds digit.