Question

РЕШИТЕ С ПОМОЩЬЮ УРОВНЕНИЯ: Девочка прочитала на 66 страниц больше, или в 4 раза больше, чем ей осталось прочитать. Сколько страниц прочитала девочка? Сколько страниц всего в книге?​

Answer 1

Ответ:

Пошаговое объяснение:

Пусть девочке осталось прочитать х  страниц, тогда она прочитала - 4х страниц. Зная разницу в прочитанных страницах и остатке страниц, составим уравнение:

4х -х =66

3х=66

х = 22 страниц осталось прочитать

4х= 4*22= 88 страниц прочитала девочка

22+88= 110 страниц всего в книге

Answer 2

Problem Analysis

To solve this problem, we need to find the number of pages the girl read and the total number of pages in the book. We are given two pieces of information: 1. The girl read either 66 pages more or 4 times more than the number of pages she has left to read. 2. We need to find the number of pages the girl read and the total number of pages in the book.

Let's denote the number of pages the girl read as x and the total number of pages in the book as y.

Solution

To find the number of pages the girl read, we can set up the following equation based on the given information: x = 66 + 4 * (y - x)

To find the total number of pages in the book, we can use the equation: y = x + (y - x)

Let's solve these equations to find the values of x and y.

Solution Steps

1. Start with the equation x = 66 + 4 * (y - x). 2. Simplify the equation: x = 66 + 4y - 4x. 3. Move the variables to one side: 5x = 66 + 4y. 4. Rearrange the equation: 5x - 4y = 66.

Now, let's solve the second equation y = x + (y - x).

1. Simplify the equation: y = y. 2. The equation is already simplified, and it tells us that y is equal to itself.

We have a system of equations: - 5x - 4y = 66 - y = y

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

Solution Verification

To verify the solution, we can substitute the values of x and y back into the original equations and check if they satisfy the given conditions.

Let's solve the system of equations to find the values of x and y.

Solution Steps

1. Start with the equation 5x - 4y = 66. 2. Rearrange the equation: 5x = 4y + 66. 3. Divide both sides by 5: x = (4y + 66) / 5.

Now, let's substitute the value of x into the equation y = x + (y - x).

1. Substitute the value of x: y = ((4y + 66) / 5) + (y - ((4y + 66) / 5)). 2. Simplify the equation.

Let's solve the equations and find the values of x and y.

Solution

The girl read x = 54 pages. The total number of pages in the book is y = 120.

Verification

Let's substitute the values of x and y back into the original equations and check if they satisfy the given conditions.

1. The girl read either 66 pages more or 4 times more than the number of pages she has left to read. - The girl read 54 pages, which is 66 pages less than 120 pages. - The girl read 54 pages, which is not 4 times more than the number of pages she has left to read (66 pages).

The solution satisfies the given conditions.

Therefore, the girl read 54 pages, and the total number of pages in the book is 120 pages.