Answer :

Let's solve this step-by-step.

1. Identify the unknowns and express them using variables:

- Let's denote the first number as [tex]\( x \)[/tex].
- The second number is 2 times the first number: [tex]\( 2x \)[/tex].
- The third number is 100 more than the first number: [tex]\( x + 100 \)[/tex].

2. Set up the equation based on the given information:

We are told that the sum of these three numbers is 440.

So, we can write the equation:
[tex]\[ x + 2x + (x + 100) = 440 \][/tex]

3. Combine like terms:

Simplify the equation by combining the [tex]\( x \)[/tex] terms:
[tex]\[ x + 2x + x + 100 = 440 \][/tex]
[tex]\[ 4x + 100 = 440 \][/tex]

4. Solve for [tex]\( x \)[/tex]:

Subtract 100 from both sides of the equation:
[tex]\[ 4x = 440 - 100 \][/tex]
[tex]\[ 4x = 340 \][/tex]

Divide both sides by 4:
[tex]\[ x = \frac{340}{4} \][/tex]
[tex]\[ x = 85 \][/tex]

So, the first number is [tex]\( x = 85 \)[/tex].

5. Find the second and third numbers:

- Second number: [tex]\( 2x = 2 \times 85 = 170 \)[/tex]
- Third number: [tex]\( x + 100 = 85 + 100 = 185 \)[/tex]

6. Summary:

- The first number is [tex]\( 85 \)[/tex].
- The second number is [tex]\( 170 \)[/tex].
- The third number is [tex]\( 185 \)[/tex].

Thus, the three numbers are [tex]\( 85 \)[/tex], [tex]\( 170 \)[/tex], and [tex]\( 185 \)[/tex], respectively.