Questions: A 22-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 1/4 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? The bookworm ate through inches of book. (Type an integer or a decimal)

Solution Steps

To determine how many inches of book the bookworm ate, we need to consider the path it takes. The bookworm starts inside the front cover of the first volume and ends after the back cover of the last volume. Since each volume is 2 inches thick and each cover is 0.25 inches thick, the bookworm does not eat through the front cover of the first volume or the back cover of the last volume. Therefore, the bookworm eats through the pages and the back cover of the first volume, the pages of all the middle volumes, and the front cover and pages of the last volume.

1. Calculate the total thickness of the encyclopedia without the first front cover and the last back cover.
2. Subtract the thickness of the first front cover and the last back cover from the total thickness.

The encyclopedia consists of 22 volumes, each with a thickness of 2 inches. Therefore, the total thickness of the encyclopedia is calculated as: \[ \text{Total Thickness} = 22 \times 2 = 44 \text{ inches} \]

Each cover is \(0.25\) inches thick. The bookworm does not eat through the front cover of the first volume and the back cover of the last volume. Thus, the thickness of these two covers is: \[ \text{Excluded Thickness} = 2 \times 0.25 = 0.5 \text{ inches} \]

The bookworm eats through the entire thickness of the encyclopedia except for the first front cover and the last back cover. Therefore, the thickness eaten by the bookworm is: \[ \text{Eaten Thickness} = 44 - 0.5 = 43.5 \text{ inches} \]

Final Answer