Question

На первой полке книг в 3 раза меньше чем на второй. Если с первой полки взять 7 книг, а на вторую поставить 9, то книг на первой полке будет в 5 раз меньше чем на второй. Сколько было книг на каждой полке?

Answer 1

Если на первой полке - х книг, то на второй - 3х.
Далее, следуя условию, если с первой взять 7 книг, то их будет х-7
Если на вторую добавить 9 книг, то их будет 3х+9
Зная, что на первой полке теперь книг в 5 раз меньше составим уравнение:
(х-7)*5=3х+9
5х-35=3х+9
5х-3х=9+35
2х=44
х=22 (книг) - было на первой полке

33*3=66 (книг) - было на второй полке

Ответ: на первой полке было 22 книги, а на второй 66 книг.

Answer 2

Problem Analysis

We are given that there are three times fewer books on the first shelf compared to 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 five times smaller than the number of books on the second shelf. We need to determine the number of books on each shelf.

Solution

Let's assume that the number of books on the first shelf is x, and the number of books on the second shelf is y.

According to the given information, we have the following equations:

1. x = y/3 (There are three times fewer books on the first shelf compared to the second shelf) 2. x + 7 = (y + 9)/5 (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 five times smaller than the number of books on the second shelf)

We can solve these equations to find the values of x and y.

Solving the Equations

From equation 1, we can substitute the value of x in equation 2:

(y/3) + 7 = (y + 9)/5

Now, let's solve this equation step by step:

1. Multiply both sides of the equation by 15 to eliminate the denominators:

5(y/3) + 5(7) = 3(y + 9)

2. Simplify:

5y/3 + 35 = 3y + 27

3. Multiply both sides of the equation by 3 to eliminate the fraction:

3(5y/3 + 35) = 3(3y + 27)

5y + 105 = 9y + 81

4. Subtract 5y from both sides of the equation:

105 = 4y + 81

5. Subtract 81 from both sides of the equation:

24 = 4y

6. Divide both sides of the equation by 4:

y = 6

Now that we have the value of y, we can substitute it back into equation 1 to find the value of x:

x = 6/3 = 2

Therefore, there are 2 books on the first shelf and 6 books on the second shelf.

Answer

There are 2 books on the first shelf and 6 books on the second shelf.