Question

Решите задачу выделяя три этапа математического моделирования. В школьной теплице ученики вырастили перец помидоры баклажаны. взвесив собранный урожай они определили что баклажанов собранно на 65 кг больше , чем перца, и в 3 раза меньше , чем помидоров. Найдите массу баклажанов, если весь урожай составил 730 кг. Помогите , очень надо!((((

Answer 1

Х-  баклажаны
х-65-перец
3х-помидоры

х+х-65+3х=730
5х=730-65
5х=665
х=665/5=133кг -  баклажаны
133-65=68-перец
133*3=399-помидоры

Answer 2

х-  баклажаны;х-65-перцы;3х-помидоры
х+х-65+3х=730
5х=730-65
5х=665
х=665:5=133кг -  баклажан
133-65=68кг-перцев
133*3=399кг-помидор

Answer 3

Mathematical Modeling of the Problem

To solve the problem of finding the mass of eggplants grown in the school greenhouse, we can break down the mathematical modeling into three main steps:

1. Defining Variables and Formulating Equations: We'll start by defining variables for the masses of peppers, tomatoes, and eggplants. Then, we'll formulate equations based on the given information about the relationship between the masses of these vegetables.

2. Solving the Equations: Next, we'll solve the system of equations to find the mass of each type of vegetable.

3. Verification and Interpretation: Finally, we'll verify the solution and interpret the results in the context of the problem.

Step 1: Defining Variables and Formulating Equations

Let's denote: - The mass of peppers as P kg - The mass of tomatoes as T kg - The mass of eggplants as E kg

Based on the given information, we can formulate the following equations: - Equation 1: The mass of eggplants is 65 kg more than the mass of peppers: E = P + 65 - Equation 2: The mass of eggplants is 3 times less than the mass of tomatoes: E = T / 3 - Equation 3: The total mass of all vegetables is 730 kg: P + T + E = 730

Step 2: Solving the Equations

We can solve the system of equations to find the mass of each type of vegetable.

Substituting the value of E from Equation 1 into Equation 3: P + T + (P + 65) = 730 2P + T + 65 = 730 2P + T = 730 - 65 2P + T = 665

Substituting the value of E from Equation 2 into Equation 3: P + T + (T / 3) = 730 P + (4T / 3) = 730 3P + 4T = 2190

Now, we have a system of two equations: 2P + T = 665 3P + 4T = 2190

Solving this system of equations will give us the values of P and T, which we can then use to find the mass of eggplants.

Step 3: Verification and Interpretation

After solving the system of equations, we can verify the obtained values of P and T by substituting them back into the original equations and ensure that they satisfy all the given conditions. Once we have the values of P and T, we can use them to find the mass of eggplants using the equation E = P + 65.

Let's proceed with solving the system of equations to find the mass of each type of vegetable.