I am a 3 digit odd umber. my tens digit is one less than my hundreds digit but two more than my ones digit. The sum of my digits is 20. who am I?

let the unit digit be x

tens digit is x+2
hundreds digit is x+3

x+3 + x+2 + x = 20
3x = 15
x = 5

number is 875

Let x = tens digit, the x + 1 = hundreds and x - 2 = ones

3x - 1 = 20

3x = 21

x = 7

x + 1 = ?

x -2 = ?

To find the answer to this question, we can start by considering the given information. Let's break it down step by step:

1. The number is a 3-digit odd number: This means that the number can range from 101 to 999.

2. The tens digit is one less than the hundreds digit: Let's represent the hundreds digit as "x." Since the tens digit is one less than x, we can represent it as "x - 1."

3. The tens digit is two more than the ones digit: Let's represent the ones digit as "y." According to this information, the tens digit can be expressed as "y + 2."

4. The sum of the digits is 20: This means that the sum of the hundreds digit, the tens digit, and the ones digit is equal to 20. So mathematically, we can write this as "x + (x - 1) + (y + 2) = 20."

Now, let's solve the equation:

2x + y + 1 = 20
2x + y = 19

Since we are dealing with whole numbers, we can substitute different values and check if it satisfies the equation.

Looking at the equation 2x + y = 19, we can see that x should be an odd number since the sum of the other two numbers is 19. We can start substituting values for x and see if it gives us a valid solution.

Let's start with x = 3:
2(3) + y = 19
6 + y = 19
y = 13

But hold on, this doesn't satisfy the other given conditions. If we plug x = 3 and y = 13 into the previous conditions, we see that "x - 1" should equal "y + 2", but that's not true here.

Let's try another value for x:

x = 5:
2(5) + y = 19
10 + y = 19
y = 9

Now, let's check if this satisfies all of the given conditions:

1. The number is a 3-digit odd number: Yes, because the number is 5xy.
2. The tens digit is one less than the hundreds digit: Yes, because x - 1 = 4, and the tens digit is 4.
3. The tens digit is two more than the ones digit: Yes, because y + 2 = 11, and the tens digit is 11.
4. The sum of the digits is 20: Yes, because 5 + 4 + 9 = 18, which matches the given information.

So, the number that satisfies all these conditions is 594.