Question

Число книг на первой полке в три раза меньше, чем на другой. Если с первой полки взять 7 книг, а на вторую поставить 9, то число книг на первой полке будет в 5 раз меньше, чем на второй. Сколько книг было на каждой полке первоначально? помогите решить!!!

Answer 1

Пусть на  первой полке  Х книг. Так как на первой полке в 3 р меньше книг , чем на второй , то на второй в 3 больше книг , чем на первой , то есть--- 3Х, если переставлять книги с первой и второй полки , получим уравнение:
3Х+9=5(Х-7)
3Х=9=5Х-35
5Х-3Х=9+35
2Х=44
Х=44:2
Х=22 ---на первой полке книг было первоначально
2) 22х3=66 (книг ) ---было первоначально на 2 полке

Answer 2

Problem Analysis

We are given that the number of books on the first shelf is three times less than the number of books on the second shelf. If we take 7 books from the first shelf and put 9 books on the second shelf, the number of books on the first shelf will be 5 times less than the number of books on the second shelf. We need to find the initial number of books on each shelf.

Solution

Let's assume the initial number of books on the second shelf is x. According to the problem, the number of books on the first shelf is three times less than the number of books on the second shelf, so the number of books on the first shelf is x - 3x = -2x.

After taking 7 books from the first shelf, the number of books on the first shelf becomes -2x - 7. After putting 9 books on the second shelf, the number of books on the second shelf becomes x + 9.

According to the problem, the number of books on the first shelf is 5 times less than the number of books on the second shelf, so we can write the equation:

-2x - 7 = 5(x + 9)

Now, let's solve this equation to find the value of x.

Solving the Equation

Simplifying the equation:

-2x - 7 = 5x + 45

Adding 2x to both sides:

-7 = 7x + 45

Subtracting 45 from both sides:

-52 = 7x

Dividing both sides by 7:

x = -52/7

So, the initial number of books on the second shelf, x, is approximately -7.43.

Now, let's find the initial number of books on the first shelf, which is -2x:

-2(-52/7) = 104/7

So, the initial number of books on the first shelf is approximately 14.86.

Therefore, the initial number of books on the first shelf was approximately 15, and the initial number of books on the second shelf was approximately -7.

Please note that it is not possible to have a negative number of books on a shelf, so the given problem may not have a valid solution.