Let's break down the problem step by step.

Let $x$ be the total number of candies in Christian's bag originally.

Step 1: After eating $\frac{1}{3}$ and giving 12 candies to Megan

• Christian ate $\frac{1}{3}$ of his candies, so the remaining candies are $\frac{2}{3}$ of $x$.
• He then gave 12 candies to Megan, so the number of candies left after these two actions is: $\frac{2}{3}x - 12$

Step 2: After eating $\frac{1}{4}$ of the remaining candies and giving 5 to Drew

• Christian ate $\frac{1}{4}$ of the remaining candies, so the number of candies he had after this is: $\left( \frac{2}{3}x - 12 \right) \times \frac{3}{4} = \frac{3}{4} \left( \frac{2}{3}x - 12 \right)$
• Simplifying: $\frac{3}{4} \times \left( \frac{2}{3}x - 12 \right) = \frac{1}{2}x - 9$
• He then gave 5 candies to Drew, so the remaining number of candies is: $\frac{1}{2}x - 9 - 5 = \frac{1}{2}x - 14$

Step 3: Sharing the remaining candies equally with Dr. Li

• Christian and Dr. Li shared the remaining candies equally. This means the total number of candies left is twice what Dr. Li ate. Dr. Li ate 20 candies, so the total number of remaining candies was $2 \times 20 = 40$.
• Thus, we have the equation: $\frac{1}{2}x - 14 = 40$

Step 4: Solving for $x$

• Add 14 to both sides: $\frac{1}{2}x = 54$
• Multiply both sides by 2: $x = 108$

Thus, the total number of candies in Christian's bag originally was 108.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:

1. What would happen if Christian ate $\frac{1}{2}$ of the candies instead of $\frac{1}{3}$ initially?
2. How would the solution change if Dr. Li ate 30 candies instead of 20?
3. What if Megan received 20 candies instead of 12? How would that affect the original amount?
4. How can we generalize this problem to any fraction of candies being eaten at each step?
5. What is the impact of Drew receiving more or fewer candies on the final solution?

Tip: Breaking down complex word problems into smaller steps makes it easier to identify and solve equations!