Question

Смесь, состоящая из двух веществ, веслиа 0.72 кг.После того как из неё выделили 40% первого вещества и 25% второго, первого вещества оказалось в смеси на 270 г больше, чем второго.Сколько весило перавначально каждое вещество,входящие в смесь?

Answer 1

х-1е в-во

у-1е в-во

состовляем систему уравнений

х+у=0.72кг

(х-0.4х)-(у-0.25у)=0.27кг

0.6х-0.75у=0.27

выражаем у из 1го уравнения

у=0.72-х

подставляем во второе уравнение

0.6х-0.75(0.72-х)=0.27

получаем х=0.6кг

у=0.15кг

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer 2

Problem Analysis

We are given a mixture consisting of two substances, and we need to determine the initial weight of each substance. After extracting 40% of the first substance and 25% of the second substance from the mixture, the weight of the first substance remaining in the mixture is 270 grams more than the weight of the second substance remaining.

Solution

Let's assume the initial weight of the first substance in the mixture is x kg, and the initial weight of the second substance is y kg.

According to the problem, the weight of the mixture is 0.72 kg. Therefore, we have the equation:

x + y = 0.72 (Equation 1)

After extracting 40% of the first substance and 25% of the second substance, the weight of the first substance remaining in the mixture is 270 grams more than the weight of the second substance remaining. Mathematically, we can express this as:

0.6x - 0.25y = 0.27 (Equation 2)

Simplifying Equation 2, we get:

6x - 2.5y = 2.7 (Equation 3)

Now, we can solve Equations 1 and 3 simultaneously to find the values of x and y.

Solving the Equations

To solve the equations, we can use the substitution method. Rearranging Equation 1, we get:

x = 0.72 - y (Equation 4)

Substituting Equation 4 into Equation 3, we have:

6(0.72 - y) - 2.5y = 2.7

Simplifying the equation:

4.32 - 6y - 2.5y = 2.7

Combining like terms:

-8.5y = -1.62

Dividing both sides by -8.5:

y = 0.19

Substituting the value of y back into Equation 4, we can find the value of x:

x = 0.72 - 0.19 = 0.53

Answer

Therefore, the initial weight of the first substance in the mixture was 0.53 kg, and the initial weight of the second substance was 0.19 kg.