Question

Помогите пожалуйста решить задачу,выделяя 3 этапа математического моделирования. В кабинете математики в трех шкафах лежат модели геометрических фигур.Во втором шкафу на 4 модели больше,чем в третьем,и на 15 меньше ,чем в первом.Сколько моделей в каждом шкафу,если всего в кабинете 50 моделей?

Answer 1

ПУСТЬ Х МОДЕЛЕЙ ВО ВТОРОМ ШКАФУ, ТОГДА Х-4 МОДЕЛЕЙ В ТРЕТЬЕМ ШКАФУ И Х+15 МОДЕЛЕЙ В ПЕРВОМ ШКАФУ.ТАК КАК ВСЕГО МОДЕЛЕЙ 50, СОСТАВИМ УРАВНЕНИЕ      Х+(Х-4)+(Х+15)=50       Х+Х-4+Х+15=50           3Х=50-15+4    3Х=39    Х=39:3   х=13  ВО ВТОРОМ ШКАФУ                                    13-4=9  В ТРЕТЬЕМ ШКАФУ         13+15=28 В ПЕРВОМ ШКАФУ

Answer 2

Mathematical Modeling Process

To solve the problem of determining the number of models in each cabinet, we can follow the three stages of mathematical modeling:

1. Formulation of the Problem: - Define the problem and the unknowns. - Translate the problem into mathematical language.

2. Solution of the Problem: - Develop a mathematical model to represent the problem. - Solve the mathematical model to find the unknowns.

3. Validation and Interpretation of Results: - Verify the solution in the context of the original problem. - Interpret the results in the context of the problem.

Formulation of the Problem

Let's denote the number of models in the first, second, and third cabinets as x, y, and z respectively. We are given the following information: - The total number of models in the cabinets is 50: x + y + z = 50 - The second cabinet has 4 more models than the third: y = z + 4 - The second cabinet has 15 fewer models than the first: y = x - 15

Solution of the Problem

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

Substituting the value of y from the second and third equations into the first equation: x + (z + 4) + z = 50 x + 2z + 4 = 50 x + 2z = 46

Substituting the value of y from the third equation into the second equation: x - 15 = z + 4 x = z + 19

Now we have two equations: x + 2z = 46 x = z + 19

Solving these equations will give us the values of x, y, and z.

Validation and Interpretation of Results

After obtaining the values of x, y, and z, we need to verify that they satisfy all the given conditions and interpret the results in the context of the problem.

Let's proceed with solving the equations to find the values of x, y, and z.