Alright, let's solve this step-by-step.
1. Identify the variables:
- Let the smaller number be [tex]\( x \)[/tex].
- Let the other number be [tex]\( y \)[/tex].
2. Set up the equations based on the problem statement:
- According to the problem, one number is 9 more than twice another number. This relationship can be expressed as:
[tex]\[
y = 2x + 9
\][/tex]
- The sum of the numbers is 129. This can be written as:
[tex]\[
x + y = 129
\][/tex]
3. Substitute the expression for [tex]\( y \)[/tex] into the second equation:
- From the first equation, we know that [tex]\( y = 2x + 9 \)[/tex]. Substitute [tex]\( y \)[/tex] in the second equation:
[tex]\[
x + (2x + 9) = 129
\][/tex]
4. Combine like terms and simplify:
- Combine [tex]\( x \)[/tex] and [tex]\( 2x \)[/tex]:
[tex]\[
3x + 9 = 129
\][/tex]
5. Isolate [tex]\( x \)[/tex] by subtracting 9 from both sides of the equation:
- Subtract 9 from both sides:
[tex]\[
3x = 120
\][/tex]
6. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 3:
- Divide both sides by 3:
[tex]\[
x = \frac{120}{3}
\][/tex]
[tex]\[
x = 40
\][/tex]
So, the smaller number is [tex]\( x = 40 \)[/tex].
