Question

Сплав весом 18 кг состоит из двух металлов. От сплава отделили 40%первого, 25% второго металла. После этого в сплаве количество двух металлов стало равным. Найдите сколько в сплаве кг было из каждого металла в начале?​

Answer 1

Ответ:

стало каждого х кг

первого было х/0,6, второго было х/0,75

х/0,6 + х/0,75 = 18

домножим на 1,5:

2,5х + 2х = 27

х = 6 кг - стало каждого

первого было х/0,6 = 10 кг

второго = х/0,75 = 8 кг

Answer 2

Problem Analysis

We are given a alloy weighing 18 kg that consists of two metals. 40% of the first metal and 25% of the second metal were separated from the alloy. After the separation, the amount of each metal in the alloy became equal. We need to find the initial weights of each metal in the alloy.

Solution

Let's assume the initial weight of the first metal in the alloy is x kg and the initial weight of the second metal is y kg.

According to the problem, 40% of the first metal and 25% of the second metal were separated from the alloy. This means that after the separation, the remaining alloy contains 60% of the first metal and 75% of the second metal.

Since the amount of each metal in the alloy became equal after the separation, we can set up the following equation:

0.6x = 0.75y

To solve this equation, we can use the fact that the total weight of the alloy is 18 kg. So we have another equation:

x + y = 18

We can solve these two equations simultaneously to find the values of x and y.

Let's solve the equations:

0.6x = 0.75y (Equation 1) x + y = 18 (Equation 2)

From Equation 2, we can express x in terms of y:

x = 18 - y

Substituting this value of x in Equation 1:

0.6(18 - y) = 0.75y

Simplifying the equation:

10.8 - 0.6y = 0.75y

Combining like terms:

10.8 = 1.35y

Dividing both sides by 1.35:

y = 10.8 / 1.35 = 8

Substituting the value of y back into Equation 2:

x + 8 = 18

Subtracting 8 from both sides:

x = 18 - 8 = 10

Therefore, the initial weight of the first metal in the alloy was 10 kg, and the initial weight of the second metal was 8 kg.

Answer: The alloy initially contained 10 kg of the first metal and 8 kg of the second metal.

Verification

Let's verify our answer using the given information.

According to the problem, 40% of the first metal and 25% of the second metal were separated from the alloy. This means that after the separation, the remaining alloy contains 60% of the first metal and 75% of the second metal.

Let's calculate the amount of each metal in the remaining alloy:

Amount of first metal in the remaining alloy = 0.6 * 10 kg = 6 kg Amount of second metal in the remaining alloy = 0.75 * 8 kg = 6 kg

As we can see, the amount of each metal in the remaining alloy is equal, which matches the given information. Therefore, our answer is verified.

Conclusion

The initial weight of the first metal in the alloy was 10 kg, and the initial weight of the second metal was 8 kg.