Question

Решите задачу,выделив три этапа математического моделирования.Маше подарили 3 коробки конфет.Во второй коробке в 2 раза меньше конфет,чем в первой,а в третьей на 10 конфет меньше чем в первой.Если в первую коробку добавить ещё 34 конфеты,то количество конфет в первой коробке будет равно количеству конфет во второй и третьей коробках вмсте.Сколько конфет бфло в каждой коробке первоначально?

Answer 1

Пусть в первой коробке было х конфет. Тогда во второй коробке было0,5х конфет, а в третьей х-10 конфет. 
Составим и решим уравнение по условию задачи: 
х+34=0,5х+х-10 
х=88 
В первой коробке 88 конфет. Во второй 44 конфеты. В третьей 78 конфет.

Answer 2

Mathematical Modeling: Three Stages

Mathematical modeling involves the process of representing real-world situations using mathematical equations and techniques. It typically consists of three stages: problem formulation, model construction, and model analysis.

1. Problem Formulation: In this stage, the problem is defined and the objectives and constraints are identified. It involves understanding the context of the problem, gathering relevant data, and determining the key variables and relationships involved. In the given problem, the objective is to determine the initial number of candies in each box, given the information provided.

2. Model Construction: Once the problem is formulated, the next step is to construct a mathematical model that represents the problem. This involves translating the real-world situation into mathematical equations or functions. In this case, we need to set up equations based on the information given about the number of candies in each box and the relationship between them.

3. Model Analysis: After constructing the mathematical model, the next step is to analyze the model to obtain the desired solution. This may involve solving equations, performing calculations, or using mathematical techniques to derive the solution. In this problem, we will use the information provided about adding 34 candies to the first box to determine the initial number of candies in each box.

Solving the Problem

Let's solve the problem step by step:

1. Let's assume the initial number of candies in the first box is x. 2. According to the problem, the second box has 2 times fewer candies than the first box. Therefore, the number of candies in the second box is x/2. 3. The third box has 10 candies fewer than the first box. Therefore, the number of candies in the third box is x - 10. 4. If we add 34 candies to the first box, the number of candies in the first box becomes x + 34. 5. According to the problem, the number of candies in the first box will be equal to the sum of the number of candies in the second and third boxes. Therefore, we can set up the equation: x + 34 = (x/2) + (x - 10).

Now, let's solve the equation to find the initial number of candies in the first box.

x + 34 = (x/2) + (x - 10)

To solve this equation, we can simplify it by multiplying through by 2 to eliminate the fraction:

2(x + 34) = x + 2(x - 10)

Simplifying further:

2x + 68 = x + 2x - 20

Combining like terms:

2x + 68 = 3x - 20

Subtracting 2x from both sides:

68 = x - 20

Adding 20 to both sides:

x = 88

Therefore, the initial number of candies in the first box was 88.

To find the number of candies in the second box, we substitute the value of x into the equation:

Number of candies in the second box = x/2 = 88/2 = 44

To find the number of candies in the third box, we substitute the value of x into the equation:

Number of candies in the third box = x - 10 = 88 - 10 = 78

Therefore, the initial number of candies in each box was: - First box: 88 candies - Second box: 44 candies - Third box: 78 candies

Please note that the solution provided is based on the information given in the problem.