Question

решите задачу,выделяя три этапа математического моделирования: книги надо разместить в нескольких ящиках стола.Если в каждый ящик класть по четыре книги,то три книги окажутся лишними.Если же в каждый ящик класть по пять книг,то двух книг в одном из ящиков будет не хватать.Сколько будет ящиков? ЗАРАНЕЕ БОЛЬШОЕ СПАСИБО!

Answer 1

х ящиков - всего

 

5х -2 (книг) - в х ящиках по 5 книг в каждом и 2 книги не хватает

4х +3 (книг) - в х ящиках по 4 книги и 3 книги лишние

 

Раскладывали одинаковое количество книг

5х+2 = 4х-3

х=5(ящиков)

Answer 2

Mathematical Modeling of Book Placement Problem

To solve the problem of placing books in multiple boxes on a table, we can break down the mathematical modeling process into three stages:

Stage 1: Problem Formulation In this stage, we define the problem and its constraints. Let's denote the number of boxes as x. We are given two conditions: 1. If we place 4 books in each box, we will have 3 extra books. 2. If we place 5 books in each box, one of the boxes will be short of 2 books.

Stage 2: Mathematical Representation In this stage, we represent the problem mathematically using equations or inequalities. Let's represent the conditions mentioned above:

Condition 1: If we place 4 books in each box, we will have 3 extra books. - Total number of books = 4x + 3

Condition 2: If we place 5 books in each box, one of the boxes will be short of 2 books. - Total number of books = 5x - 2

Stage 3: Solution In this stage, we solve the mathematical representation to find the solution. We need to find the value of x that satisfies both conditions simultaneously.

By equating the two expressions for the total number of books, we can solve for x:

4x + 3 = 5x - 2

Simplifying the equation, we get:

x = 5

Therefore, the number of boxes required to satisfy the given conditions is 5.

Please note that the sources provided did not contain specific information related to this mathematical modeling problem. The solution is derived solely based on the given problem statement and mathematical reasoning.

I hope this helps! Let me know if you have any further questions.