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)

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

failed
failed

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.
Step 1: Calculate Total Thickness of the Encyclopedia

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

Step 2: Calculate Thickness of Excluded Covers

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: \[ \text{Excluded Thickness} = 2 \times 0.25 = 0.5 \text{ inches} \]

Step 3: Calculate Thickness Eaten by the Bookworm

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

\(\boxed{43.5}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
d) La inversa (si la tiene) de D(t), para el dominio y recorrido considerados. La inversa de la función D(t)=0,058 · t+1,12 es D^-1(t)=(t-1,12)/0,058
failedAnswered
Part D - LO 4, Describe the Process by Which Oxidation Can Damage Cells and the Role of Antioxidants in Opposing This Damage Antioxidants can work as vitamins, as phytochemicals, and as mineral cofactors within antioxidant enzyme systems. Complete the sentence below about the various functions of antioxidants. Antioxidants do not help stabilize free radicals increase oxidative damage convert free radicals to less damaging substances donate electrons Submit Request Answer Part E - LO 5, Identify the Antioxidant Functions of Key Micronutrients and Carotenoids Oct 27 5: 22
failedAnswered
How does stigma related to certain diseases, like HIV, impact public health efforts? Criminalizing HIV transmission encourages more people to seek testing and treatment. What is one ethical concern about the secondary use of newborn bloodspot samples for research?
failedAnswered
Simplify the expression: 72 ÷ 9 · 3 =
failedAnswered
Simplify each expression. Assume that the variables represent any real numbers. Use the absolute value button only when necessary. (a) sqrt(y^6) = y^3 (b) sqrt(212) = .