i am a 3 digit number,my ones digit is twice my hundreds digit,when rounded to the nearest hundred i round to 500,my tens digit is less than 6,what number am i?

Suppose the number is ABC. Then if C is twice A, we know that A can't be any greater than 4. So the number must be one of the following: 1B2, 2B4, 3B6 or 4B8. When rounded to the nearest hundred it's 500, so it must be the last of those four, i.e. 4B8. If the tens digit is less than 6 then the number must be 408, 418, 428, 438, 448 or 458. All of these would round to 400 except the last one, so the answer must be 458.

Let's solve this step-by-step.

Step 1: The ones digit is twice the hundreds digit.
Let's express the ones digit as x and the hundreds digit as y.
Based on the given information, we can write the equation: x = 2y.

Step 2: When rounded to the nearest hundred, the number rounds to 500.
This means the number is between 450 and 549.

Step 3: The tens digit is less than 6.
Let's express the tens digit as z.
Based on the given information, we can write the inequality: z < 6.

Step 4: Combining all the information.
The number can be written as 100y + 10z + x.

From Step 1, we know that x = 2y.
From Step 2, we know that 100y + 10z + x is between 450 and 549.
From Step 3, we know that z < 6.

Now we can substitute the values and solve for the number.

450 ≤ 100y + 10z + x ≤ 549
Substituting x = 2y:
450 ≤ 100y + 10z + 2y ≤ 549

Simplifying the expression:
450 ≤ 102y + 10z ≤ 549

Since the tens digit, z, is less than 6, the highest possible value for z is 5.

Now we can try all the possible values for y and z, and check if the above inequality holds true:

For y = 4 and z = 5:
450 ≤ 102(4) + 10(5) ≤ 549
450 ≤ 408 + 50 ≤ 549
450 ≤ 458 ≤ 549

The number is between 450 and 549, so it satisfies the second condition.
The tens digit is less than 6, so it satisfies the third condition.

Therefore, the number is 458.

To solve this problem, let's break it down step by step:

Step 1: Start with the given information.
We know that the number is a 3-digit number and when rounded to the nearest hundred, it rounds to 500.

Step 2: Determine the hundreds digit.
Since rounding to the nearest hundred gives us 500, we know that the number must be between 450 and 550. Therefore, the hundreds digit must be 5.

Step 3: Determine the tens digit.
We are given that the tens digit is less than 6. Since the hundreds digit is 5, the number can only be 50x or 51x, where x represents the unknown ones digit.

Step 4: Determine the ones digit.
The problem states that the ones digit is twice the hundreds digit. Since the hundreds digit is 5, the ones digit must be 2 times 5, which is 10.

Step 5: Combine the digits to find the number.
The hundreds digit is 5, the tens digit is 1, and the ones digit is 0. Therefore, the number is 510.

So, the answer is 510.