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The problem asks us to write and solve an absolute value equation to represent how many gallons of gas Hugo will pump when the total is $25, plus or minus $0.50.

### Given Information:
- Hugo is pumping **regular gas**.
- Regular gas costs **$2.50 per gallon**.
- The total cost is **$25**, with an acceptable deviation of **plus or minus $0.50**.

### Let $ x $ be the number of gallons of gas.

The equation for the total cost is:
\[
\text{Total cost} = 2.50 \times x
\]

We are told that the total cost can range from **$24.50** to **$25.50** (because $25 \pm 0.50$).

### Absolute Value Equation:
We express this situation using an absolute value equation. The equation should represent the total being within $0.50 of $25:
\[
|2.50x - 25| = 0.50
\]

### Solving the Equation:
1. Remove the absolute value by considering two cases:
   \[
   2.50x - 25 = 0.50 \quad \text{or} \quad 2.50x - 25 = -0.50
   \]

2. Solve each equation:
   - For $ 2.50x - 25 = 0.50 $:
     \[
     2.50x = 25.50 \quad \Rightarrow \quad x = \frac{25.50}{2.50} = 10.2 \, \text{gallons}
     \]
   - For $ 2.50x - 25 = -0.50 $:
     \[
     2.50x = 24.50 \quad \Rightarrow \quad x = \frac{24.50}{2.50} = 9.8 \, \text{gallons}
     \]

### Final Answer:
Hugo will pump between **9.8 gallons and 10.2 gallons** of regular gas.

Would you like further details or have any questions?

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Here are 5 questions to expand this topic:
1. How would the equation change if Hugo pumped premium gas instead?
2. How can you interpret the solution graphically on a number line?
3. What is the general form of absolute value equations and how are they solved?
4. How do you solve absolute value inequalities, such as if the total could exceed $25.50?
5. How would you check if the solution is correct by substitution?

**Tip:** Always check both cases when solving absolute value equations to ensure the correct range of values!

Hugo is pumping regular gas into his truck. Write and solve an absolute value equation to represent how many gallons of gas will be pumped when the total is $25 plus or minus $0.50.

Solve an absolute value equation to determine the number of gallons of regular gas pumped for a total cost of $25, plus or minus $0.50. This problem covers key algebraic concepts involving absolute value equations and basic linear equations, suitable for Grades 8-10.

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