A 25​-volume encyclopedia is placed on a bookshelf in numerical order from left to right. Each volume is 2 inches​ thick, including the front and back covers. Each cover is one fourth
 inch thick. The volumes are placed on the shelf so that the front cover is on the right side of each volume and the back cover is on the left side of each volume. A bookworm eats straight through the​ encyclopedia, beginning inside the front cover of the first volume and ending after eating through the back cover of the last volume. How many inches of book did the bookworm​ eat?

Let's break down the problem to find out how many inches the bookworm eats through.

### Key information:
- There are 25 volumes, each 2 inches thick.
- Each volume has a front cover and a back cover, each of which is \( \frac{1}{4} \) inch thick.
- The bookworm starts **inside** the front cover of the **first volume** and ends after eating through the back cover of the **last volume**.

### Step-by-step solution:
1. **Understanding the bookworm’s path**:
   - The bookworm starts inside the front cover of the first volume, which means it doesn’t eat through the first front cover.
   - It stops after it eats through the back cover of the last volume, which means it doesn’t eat through the last back cover either.

2. **What the bookworm eats through**:
   - The bookworm eats through all the volumes except for the first front cover and the last back cover.
   - For all other parts of the encyclopedia, it eats through the entire thickness of each volume, including the covers.

3. **Calculating the distance covered**:
   - The total thickness of the 25 volumes:  
     \[
     25 \, \text{volumes} \times 2 \, \text{inches/volume} = 50 \, \text{inches}
     \]
   - However, since the bookworm doesn’t eat the front cover of the first volume and the back cover of the last volume, we subtract their thickness:
     \[
     50 \, \text{inches} - \left(\frac{1}{4} \, \text{inch} + \frac{1}{4} \, \text{inch}\right) = 50 \, \text{inches} - \frac{1}{2} \, \text{inch} = 49.5 \, \text{inches}
     \]

### Conclusion:
The bookworm eats through **49.5 inches** of the encyclopedia.

Would you like further explanation on any step? 

Here are 5 related questions to consider:
1. How would the solution change if the bookworm started at the back cover of the first volume instead?
2. What if each cover was \( \frac{1}{2} \) inch thick instead of \( \frac{1}{4} \)?
3. How would the answer differ if there were 30 volumes in the encyclopedia?
4. Can you calculate how many inches the bookworm eats if the front and back covers are \( \frac{1}{8} \) inch thick?
5. How many inches would the bookworm eat if it started at the front cover of the first volume and ate through to the front cover of the last volume?

**Tip**: Always subtract the portions of the object that the problem specifies as not being eaten or traveled through to avoid overestimations.

A 25​-volume encyclopedia is placed on a bookshelf in numerical order from left to right. Each volume is 2 inches​ thick, including the front and back covers. Each cover is one fourth inch thick. The volumes are placed on the shelf so that the front cover is on the right side of each volume and the back cover is on the left side of each volume. A bookworm eats straight through the​ encyclopedia, beginning inside the front cover of the first volume and ending after eating through the back cover of the last volume. How many inches of book did the bookworm​ eat?

Solve the problem of a bookworm eating through a 25-volume encyclopedia, each 2 inches thick. Learn how to calculate the total distance covered by the bookworm and how to subtract the portions not eaten. This math problem covers concepts like measurement, subtraction, and basic geometry. Suitable for Grades 5-7.

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