Let the total number of pieces of candy in the box when Morgan bought it be $x$.

Step 1: Understanding the situation

• After the movie, Morgan had half of the box of candy left. That means she had $\frac{x}{2}$ pieces remaining.
• On her way home, she ate half of that amount, which means she ate $\frac{1}{2} \times \frac{x}{2} = \frac{x}{4}$ pieces.
• After eating that, she still had 8 pieces left to give to her brother.

Step 2: Setting up the equation

The number of pieces left after she ate $\frac{x}{4}$ pieces is: $\frac{x}{2} - \frac{x}{4} = 8$

Step 3: Solving the equation

To subtract the fractions on the left side, we need a common denominator: $\frac{x}{2} - \frac{x}{4} = \frac{2x}{4} - \frac{x}{4} = \frac{x}{4}$ Thus, the equation becomes: $\frac{x}{4} = 8$

Step 4: Solving for $x$

Multiply both sides of the equation by 4 to solve for $x$: $x = 8 \times 4 = 32$

Final Answer:

There were 32 pieces of candy in the box when Morgan bought it.

Would you like further clarification or more details?

Here are 5 related questions to expand your understanding:

1. How would the problem change if Morgan had 12 pieces left instead of 8?
2. What if Morgan had eaten 3/4 of the candy she had left after the movie?
3. Can you set up and solve a similar problem if Morgan gave some of the candy to a friend?
4. How many pieces of candy would be left if she ate 3/5 of the remaining candy instead of half?
5. What fraction of the original candy did Morgan give to her little brother?

Tip: When solving word problems, try breaking the situation down step by step and using equations to represent each part of the scenario.