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.
