Question

Решите задачу . При решении используюте этапы матиматического моделирования. В библиотеке выдали книги 6,7 и 8 классам. 6 классу раздали в 1.5 раза большще книг, чем 7 классу и на 40 книг больше , чем 8 классу. сколько книг выдали каждому классу, если всего выдали 400 книг?

Answer 1

Пусть х книг выдали 7 классу
тогда 1,5*х выдали 6 классу
и 1,5х-40 выдали 8 Классу
составим уравнение
х+1.5х+1.5х-40=400
4х=440
х=110 книг выдали 7 кл.
1.5*110=165 книг выдали 6 классу
165-40=125 книг выдали 8 классу
проверка
110+165+125=400

Answer 2

Mathematical Modeling Steps for Library Book Distribution

To solve the problem of distributing books to the 6th, 7th, and 8th grades, we can follow these mathematical modeling steps:

1. Define Variables: - Let's denote the number of books given to the 7th grade as x. - The number of books given to the 6th grade is 1.5 times the number given to the 7th grade, so it is 1.5x. - The number of books given to the 8th grade is 40 less than the number given to the 6th grade, so it is 1.5x - 40. - The total number of books given out is 400.

2. Formulate Equations: - The sum of the books given to each grade equals the total number of books: - x + 1.5x + (1.5x - 40) = 400

3. Solve Equations: - Solve the equation to find the value of x and then calculate the number of books for each grade.

Solution

Let's solve the equation: - x + 1.5x + (1.5x - 40) = 400 - 4x - 40 = 400 - 4x = 440 - x = 110

Now we can calculate the number of books for each grade: - 6th grade: 1.5x = 1.5 * 110 = 165 books - 7th grade: x = 110 books - 8th grade: 1.5x - 40 = 1.5 * 110 - 40 = 165 - 40 = 125 books

So, the number of books given to each grade is: - 6th grade: 165 books - 7th grade: 110 books - 8th grade: 125 books

This solution ensures that the total number of books distributed is 400, as required.

Answer 3

Mathematical Modeling of Book Distribution to Classes

To solve the problem of distributing books to different classes, we can use mathematical modeling to represent the given information and solve for the number of books distributed to each class.

1. Representing the Given Information: - Let's denote the number of books given to the 7th class as x. - Then, the number of books given to the 6th class is 1.5x + 40. - The total number of books distributed is given as 400.

2. Formulating the Equations: - We can set up the following equations based on the given information: - x + (1.5x + 40) + x = 400

3. Solving the Equations: - We can solve the equation to find the value of x, which represents the number of books given to the 7th class.

4. Calculating the Number of Books for Each Class: - Once we find the value of x, we can calculate the number of books given to each class.

Let's proceed with solving the equation to find the number of books given to each class.