Question

A 26​-volume encyclopedia is placed on a bookshelf in numerical order. Each volume is 3 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?

Answer 1

The bookworm ate through a total of 65.5 inches of book, which includes the pages of the 26-volume encyclopedia and the extra front and back covers.

Step-by-step explanation:

To solve how many inches the bookworm ate through the 26-volume encyclopedia, first, we need to determine the total thickness of all the pages that the bookworm would have to eat through. Since we know that each volume is 3 inches thick, including the front and back covers and each cover is 1/4 inch thick, we can calculate the thickness of the pages alone in each volume by subtracting the thickness of the two covers from the total thickness of each volume.

For each volume:

• Thickness of pages only = Total thickness of a volume - Thickness of both covers
• Thickness of pages only = 3 inches - 2(1/4 inch)
• Thickness of pages only = 3 inches - 1/2 inch
• Thickness of pages only = 2.5 inches

Since there are 26 volumes, the total thickness of all the pages is 26 volumes * 2.5 inches per volume.

Total thickness of pages = 26 volumes * 2.5 inches/volume = 65 inches

However, the bookworm starts inside the front cover of the first volume and ends after eating through the back cover of the last volume. Therefore, we need to add the thickness of these two additional covers to our total.

Total inches the bookworm ate = Total thickness of pages + Thickness of the front cover of the first volume + Thickness of the back cover of the last volume

Total inches the bookworm ate = 65 inches + 1/4 inch + 1/4 inch

Total inches the bookworm ate = 65.5 inches

Answer 2

The encyclopedia has 26 volumes, each 3 inches thick. Since each volume has a front and back cover that is 1/4 inch thick, the actual pages in each volume are 3 - 1/4 - 1/4 = 2 1/2 inches thick.

To find the total thickness of all the pages in the encyclopedia, we can multiply the thickness of one volume by the number of volumes:

Total thickness of pages = 2 1/2 inches/volume x 26 volumes = 65 inches

Since the bookworm ate through the front cover of the first volume and the back cover of the last volume, it did not eat through 2 1/2 inches of pages for those volumes. Therefore, the bookworm ate through:

65 inches - 2 1/2 inches - 2 1/2 inches = 60 inches

So the bookworm ate through 60 inches of book.