To solve for \( a \) in the equation:

\[
a + a + 100 = 180
\]

### Step-by-Step Solution:

1. Combine the terms with \( a \):
   \[
   2a + 100 = 180
   \]

2. Subtract 100 from both sides:
   \[
   2a = 80
   \]

3. Divide both sides by 2 to isolate \( a \):
   \[
   a = 40
   \]

### Final Answer:
\[
a = 40
\]

Would you like further details or have any questions?

### Related Questions:
1. What is the value of \( a \) if the equation changes to \( 3a + 100 = 180 \)?
2. How would the solution change if the constant was 200 instead of 100?
3. If \( a + a + 100 = b \), and \( b = 180 \), can you find \( b \) in terms of \( a \)?
4. What happens if we add an extra term, say \( a + a + a + 100 = 180 \)?
5. How does this solution apply in different real-world contexts, such as budgeting or measurements?

### Tip:
When combining terms in an equation, always simplify like terms first.

Learn how to solve the linear equation a + a + 100 = 180 with a detailed, step-by-step solution. This problem focuses on algebraic concepts like combining like terms and solving simple linear equations. Ideal for students in Grades 6-8.

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