the thickness of a book is determined by the thickness of its cover and its pages. the front and back covers of a book like this one are each about 3 mm thick and every 25 pages adds an additional millimeter to the thickness. let nb be the number of pages and t be its thickness.

a) how thick would a 600 page book be?
b) if total thickness it to be under 48 mm, what is the largest number of pages that can be in the book?
c) give an equation relating n to T

a) To determine the thickness of a 600-page book, we need to consider the thickness of its covers and pages.

Each cover is about 3 mm thick, and since there are two covers (front and back), the total thickness from the covers is 3 mm x 2 = 6 mm.

For every 25 pages, an additional millimeter is added to the thickness. Thus, the number of additional millimeters contributed by the pages is 600 pages / 25 pages = 24 mm.

To find the total thickness, we add the thickness from the covers and the thickness from the pages: t = 6 mm + 24 mm = 30 mm.

Therefore, a 600-page book would be approximately 30 mm thick.

b) If we want the total thickness to be under 48 mm, we need to determine the maximum number of pages that can be in the book.

Again, the total thickness from the covers would be 6 mm.

Let's assume the number of additional millimeters contributed by the pages is n mm.

The equation to represent the total thickness is: t = 6 mm + n mm.

Since we want the total thickness to be less than 48 mm, we can set up the inequality: t < 48 mm.

Substituting the equation for the total thickness, we get: 6 mm + n mm < 48 mm.

Simplifying the inequality, we subtract 6 mm from both sides: n mm < 42 mm.

To find the maximum number of pages, we divide 42 mm by the mm contributed by each set of 25 pages: n mm / (25 pages) = 42 mm / (1 mm/25 pages).

Simplifying, we get: n mm / 25 pages < 42 mm * 25 pages/mm.

Canceling out the units, we have: n < 42 * 25.

Solving the inequality, we find that the largest number of pages that can be in the book while maintaining a thickness under 48 mm is n < 1050.

c) The equation relating n (number of pages) to t (thickness) can be written as follows:

t = 6 mm + (n / 25) mm.

In this equation, we divide n by 25 to determine the number of millimeters contributed by the pages. Adding this to the thickness of the covers (6 mm) gives us the total thickness.

To determine the thickness of a book, we need to consider the thickness of its covers and its pages.

Let's break down the problem and solve each part of it:

a) To find the thickness of a 600-page book, we'll start with the thickness of the covers, which are each about 3 mm thick. Therefore, the total thickness of the covers is 3 mm + 3 mm = 6 mm.
Now, for every 25 pages, the thickness increases by 1 mm. Since we have 600 pages, we can calculate the number of millimeters added due to the pages:
Additional thickness due to pages = (600 pages) / (25 pages per 1 mm) = 24 mm.
To find the total thickness, we add the thickness of the covers to the additional thickness due to the pages:
Total thickness = 6 mm + 24 mm = 30 mm.

b) If the total thickness of the book needs to be under 48 mm, we can set up an inequality to find the largest number of pages that can be in the book:
Thickness of covers = 3 mm + 3 mm = 6 mm.
Additional thickness due to pages = (25 pages) * (1 mm per 25 pages) = 1 mm.
Let's assume the number of additional millimeters due to pages is n, and the number of pages is p:
6 mm + n mm <= 48 mm.
Simplifying the inequality:
n <= 48 mm - 6 mm.
n <= 42 mm.
Now, we can find the largest number of pages by calculating the maximum number of 25-page increments that gives a total of 42 mm or less:
Number of pages = (42 mm) / (1 mm per 25 pages) = 42 * 25 = 1050 pages.

c) To give an equation relating the number of pages (n) to the total thickness (T), we can use the information provided. Let's assume the thickness of the covers is 6 mm and the additional thickness due to pages is 1 mm per 25 pages:
T = 6 + (n / 25).
This equation gives the total thickness in millimeters as a function of the number of pages.

You have the thickness of the two covers (6mm) with an additional Nmm for every 25 pages.

T = 6mm + Nmm/25

With the formula, you should be able to answer the other two questions.

I hope this helps. Thanks for asking.