Question

На трёх полках находится 75 книг. На первой полке в два раза больше книг, чем на второй, а на третьей - на 5 книг меньше, чем на первой. Сколько книг на каждой полке?

Answer 1

Problem Analysis

We are given the following information: - There are three shelves. - The first shelf has twice as many books as the second shelf. - The third shelf has 5 fewer books than the first shelf.

We need to determine the number of books on each shelf.

Solution

Let's assume the number of books on the second shelf is x.

According to the given information: - The first shelf has twice as many books as the second shelf, so it has 2x books. - The third shelf has 5 fewer books than the first shelf, so it has 2x - 5 books.

To find the total number of books, we add up the number of books on each shelf:

x + 2x + (2x - 5) = 75

Simplifying the equation:

5x - 5 = 75

Adding 5 to both sides:

5x = 80

Dividing both sides by 5:

x = 16

Now we can substitute the value of x back into the equations to find the number of books on each shelf:

- The first shelf: 2x = 2 * 16 = 32 books. - The second shelf: x = 16 books. - The third shelf: 2x - 5 = 2 * 16 - 5 = 27 books.

Therefore, there are 32 books on the first shelf, 16 books on the second shelf, and 27 books on the third shelf.

Answer

There are 32 books on the first shelf, 16 books on the second shelf, and 27 books on the third shelf.