Question

На двух полках 55 книг. Если переставить со второй полки половину книг на первую, то на первой станет в 4 раза больше книг, чем останется на второй. Сколько книг на каждой полке?

Answer 1

На второй полке Х книг ; на первой полке ( 55 - Х ) книг
4( Х - 0,5x ) = ( 55 - Х ) + 0,5х
4 • 0,5х = 55 - 0,5х
2х + 0,5х = 55
2,5х = 55
Х = 22 ( книги ) на второй
55 - 22 = 33 ( книги ) на первой
Ответ 33 книги и 22 книги были первоначально на каждой полке

Answer 2

Problem Analysis

We are given that there are 55 books on two shelves. If we move half of the books from the second shelf to the first shelf, the number of books on the first shelf will be four times greater than the number of books remaining on the second shelf. We need to determine how many books are on each shelf.

Solution

Let's assume that there are x books on the first shelf and y books on the second shelf.

According to the given information, if we move half of the books from the second shelf to the first shelf, the number of books on the first shelf will be four times greater than the number of books remaining on the second shelf. Mathematically, this can be represented as:

x + (y/2) = 4(y/2)

Simplifying the equation, we get:

x + (y/2) = 2y

Multiplying both sides of the equation by 2 to eliminate the fractions, we get:

2x + y = 4y

Rearranging the equation, we get:

2x = 3y

Now, we know that there are a total of 55 books on both shelves. So, we can write another equation:

x + y = 55

We have a system of two equations with two variables. We can solve this system of equations to find the values of x and y.

Solving the System of Equations

To solve the system of equations, we can use the substitution method. We can solve one equation for one variable and substitute it into the other equation.

From the equation 2x = 3y, we can solve for x:

x = (3y)/2

Substituting this value of x into the equation x + y = 55, we get:

(3y)/2 + y = 55

Multiplying both sides of the equation by 2 to eliminate the fraction, we get:

3y + 2y = 110

Combining like terms, we get:

5y = 110

Dividing both sides of the equation by 5, we get:

y = 22

Substituting this value of y back into the equation x + y = 55, we get:

x + 22 = 55

Subtracting 22 from both sides of the equation, we get:

x = 33

Therefore, there are 33 books on the first shelf and 22 books on the second shelf.

Answer

There are 33 books on the first shelf and 22 books on the second shelf.