Question

В овощном магазине всего330 кг яблоки груш,410кг яблок и апельсинов,и 320 кг груш и апельсинов.Сколько кг фруктов каждого вида в овощном магазине. Сколько способов решения у этой задачи? Заранее спасибо.

Answer 1

330+320=650(кг)-груш+груш+апельсины+яблоки
650-410=240(кг)-груши+груши
240:2=120(кг)-груши
330-120=210(кг)-яблоки
410-210=200(кг)-апельсины

210+120=330, 200+210=410, 120+200=320-проверка

 

или так

пусть х кг- груш 
(330-х) кг -яблок 
410-(330-х)=(80+х)кг - апельсинов =(410-х) кг 
80+х=410-х 
2х=240 
х=120 кг груш 
330-120=210 кг яблок 
410-210=200 кг апельсин

Answer 2

Problem Analysis

To solve this problem, we need to determine the weight of each type of fruit (apples, pears, and oranges) in the vegetable store. We are given the following information: - The total weight of apples and pears is 330 kg. - The total weight of apples and oranges is 410 kg. - The total weight of pears and oranges is 320 kg.

We need to find the weight of each type of fruit and determine the number of possible solutions for this problem.

Solution

Let's assume the weight of apples is A kg, the weight of pears is P kg, and the weight of oranges is O kg.

From the given information, we can form the following equations: 1. A + P = 330 (equation 1) 2. A + O = 410 (equation 2) 3. P + O = 320 (equation 3)

To solve these equations, we can use a method called substitution. We can solve equation 1 for A and substitute it into equations 2 and 3.

From equation 1, we have A = 330 - P. Substituting this into equations 2 and 3, we get: - (330 - P) + O = 410 (equation 4) - P + O = 320 (equation 5)

Now we have a system of two equations with two variables (P and O). We can solve this system to find the values of P and O.

Adding equations 4 and 5, we get: - 330 - P + P + O + O = 410 + 320 - 2O = 730 - 330 - 2O = 400 - O = 200

Substituting the value of O into equation 5, we get: - P + 200 = 320 - P = 320 - 200 - P = 120

Now that we have the values of P and O, we can substitute them back into equation 1 to find the value of A: - A + 120 = 330 - A = 330 - 120 - A = 210

Therefore, the weight of apples is 210 kg, the weight of pears is 120 kg, and the weight of oranges is 200 kg.

Number of Solutions

Now let's determine the number of possible solutions for this problem. We have found one solution where the weight of apples is 210 kg, the weight of pears is 120 kg, and the weight of oranges is 200 kg.

To determine the number of solutions, we need to check if there are any additional values of A, P, and O that satisfy the given equations. However, in this case, there is only one unique solution. This is because we have three equations and three variables, and the system of equations is consistent and independent.

Therefore, there is only one solution to this problem.

Conclusion

In the vegetable store, there are 210 kg of apples, 120 kg of pears, and 200 kg of oranges. There is only one solution to this problem.

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