Question

Задача повышенной трудности!!* Помогите решить мне , в голову не чего не приходит! В магазин привезли 8,2 т картофеля,моркови,лука и помидоров.Картофеля и моркови привезли 4,75 т, картофеля и лука - 6,37 т, картофеля и помидоров - 4,28 т. Сколько тонн каждого из овощей привезли в магазин?

Answer 1

X------картофель
y------морвовь
c-----лук
d-----помидор
1)x+y+c+d=8,2т
x+y=4,75------y=4,75-x
x+c=6,37------c=6,37-x
x+d=4,28------d=4,28-x
подставим в первое уравнение
x+4,75-x+6,37-x+4,28-x=8,2
15,4-2x=8,2
15,4-8,2=2x
7,2=2x
x=3,6т картофеля
4,75-3,6=1,15т моркови
6,37-3,6=2,77т лука
4,28-3,6=0,68т помидор

Answer 2

Problem Analysis

To solve this problem, we need to determine the amount of each vegetable (potatoes, carrots, onions, and tomatoes) that was delivered to the store. We are given the total weight of the combined deliveries of potatoes, carrots, onions, and tomatoes, as well as the weights of the combined deliveries of potatoes with each individual vegetable.

Let's break down the given information:

- Total weight of potatoes, carrots, onions, and tomatoes delivered to the store: 8.2 tons. - Weight of potatoes and carrots delivered together: 4.75 tons. - Weight of potatoes and onions delivered together: 6.37 tons. - Weight of potatoes and tomatoes delivered together: 4.28 tons.

We need to find the weight of each vegetable individually.

Solution

Let's assign variables to represent the weights of each vegetable:

- Let's assume the weight of potatoes is represented by p tons. - The weight of carrots will be represented by c tons. - The weight of onions will be represented by o tons. - The weight of tomatoes will be represented by t tons.

Using the given information, we can set up the following equations:

1. The total weight of all vegetables is 8.2 tons: p + c + o + t = 8.2.

2. The weight of potatoes and carrots combined is 4.75 tons: p + c = 4.75.

3. The weight of potatoes and onions combined is 6.37 tons: p + o = 6.37.

4. The weight of potatoes and tomatoes combined is 4.28 tons: p + t = 4.28.

We can solve this system of equations to find the values of p, c, o, and t.

Solving the Equations

To solve the system of equations, we can use substitution or elimination. Let's use the substitution method.

From equation 2, we can express c in terms of p: c = 4.75 - p.

Substituting this value of c into equations 1, 3, and 4, we get:

1. p + (4.75 - p) + o + t = 8.2. 2. p + o = 6.37. 3. p + t = 4.28.

Simplifying equation 1, we have: 4.75 + o + t = 8.2 - p.

Now we have two equations with two variables:

1. p + o = 6.37. 2. p + t = 4.28 - 4.75 + p.

Simplifying equation 2, we get: t = -0.47.

Substituting this value of t into equation 1, we have: p + o = 6.37.

Now we have one equation with one variable:

1. p + o = 6.37.

Solving for o, we get: o = 6.37 - p.

Substituting this value of o into equation 1, we have: p + (6.37 - p) = 6.37.

Simplifying, we find: p + 6.37 - p = 6.37.

The p terms cancel out, leaving us with: 6.37 = 6.37.

This equation is true for any value of p. Therefore, there are infinitely many solutions to this system of equations.

Conclusion

Based on the given information, we cannot determine the exact weights of each vegetable (potatoes, carrots, onions, and tomatoes) that were delivered to the store. The system of equations has infinitely many solutions, and we cannot uniquely determine the values of p, c, o, and t.

Please let me know if there is anything else I can help you with!