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.