To solve this, let's define the total number of pages in the book as $x$.

From the problem:

• The child has read $\frac{2}{3}$ of the book, which means the number of pages read is $\frac{2}{3}x$.
• The unread part of the book is $\frac{1}{3}x$.
• The number of pages read is 100 pages more than the unread part.

This gives us the equation: $\frac{2}{3}x = \frac{1}{3}x + 100$

Now, let's solve this equation:

1. Subtract $\frac{1}{3}x$ from both sides: $\frac{2}{3}x - \frac{1}{3}x = 100$ $\frac{1}{3}x = 100$

2. Multiply both sides by 3 to solve for $x$: $x = 300$

Thus, the total number of pages in the book is 300.

The correct answer is A. 300.

Would you like further clarification or details on any steps? Here's a few more questions that could be interesting:

1. What happens if the ratio of the read pages to unread pages is changed to 3:2?
2. How would this problem change if the read part was less than the unread part?
3. If the book has 300 pages, how many pages has the child read?
4. How can we use algebraic equations to solve similar real-life problems?
5. What other methods can we use to solve such a problem without using algebra?

Tip: In problems involving fractions of a whole, setting up equations based on the parts and whole is often the most direct path to the solution!