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To solve this problem, let's break it down step-by-step.

### Problem Summary
Allie’s counselor initially places an unknown number of chocolate bars, \( b \), on the table. Allie takes \( \frac{1}{2} \) of a chocolate bar, and after that, \( 2 \frac{1}{2} \) (or \( \frac{5}{2} \)) chocolate bars remain on the table.

### Formulating the Equation
Since Allie takes \( \frac{1}{2} \) of a chocolate bar, the equation to represent this scenario is:
\[
b - \frac{1}{2} = 2 \frac{1}{2}
\]

Thus, the correct answer from the options provided is:
\[
b - \frac{1}{2} = 2 \frac{1}{2}
\]

### Solving for \( b \)
1. Convert \( 2 \frac{1}{2} \) to an improper fraction: \( 2 \frac{1}{2} = \frac{5}{2} \).
2. Substitute into the equation:
   \[
   b - \frac{1}{2} = \frac{5}{2}
   \]
3. Add \( \frac{1}{2} \) to both sides:
   \[
   b = \frac{5}{2} + \frac{1}{2} = \frac{6}{2} = 3
   \]

Therefore, the counselor initially put **3 chocolate bars** on the table.

Would you like more details, or have any questions?

---

1. How do you convert mixed numbers to improper fractions?
2. Why do we add \( \frac{1}{2} \) to both sides in the equation?
3. What if Allie had taken a different amount of chocolate? How would that affect the equation?
4. Can we solve similar problems using subtraction or addition equations with fractions?
5. How can we check our answer for correctness?

**Tip:** When solving fraction equations, convert mixed numbers to improper fractions for easier calculations.

On bonfire night at sleepaway camp, Allie's counselor puts marshmallows, graham crackers, and several chocolate bars on the snack table. Allie uses 1/2 of a chocolate bar to make herself a s'more. Now 2 1/2 chocolate bars remain on the table. Which equation can you use to find the number of chocolate bars b the counselor puts on the table?

Learn how to solve for the initial number of chocolate bars on the table using basic algebra and fractions. This problem explores concepts such as fractions and equation solving, suitable for Grade 5 students.

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