Question

3. Есть два сплава, состоящие из меди и олова. Первый сплав содержит 40%, а второй 32% меди. По сколько килограммов нужно взять из каждого сплава, чтобы получить сплав весом 8 кг, который содержит 35% меди?

Answer 1

Ответ:

3 кг первого сплава

5 кг второго сплава

Пошаговое объяснение:

Пусть х кг нужно взять первого сплава.

тогда 0,4х - масса меди

Пусть у кг  нужно взять второго сплава

0,32y - масса меди

х+y=8 масса нового сплава

0,4х+0,32y - масса меди

0,35*8=2,8

x+y=8        

0,4х+0,32y=2,8

x+y=8        

4х+3,2y=28

x+y=8        

х+0,8y=7

0,2y=1  y=5 x=8-5=3

Answer 2

Problem Analysis

We are given two alloys, each consisting of copper and tin. The first alloy contains 40% copper, while the second alloy contains 32% copper. We need to determine how many kilograms of each alloy should be taken to obtain an 8 kg alloy that contains 35% copper.

Solution

Let's assume that x kilograms of the first alloy and y kilograms of the second alloy are taken to obtain the desired alloy.

To solve this problem, we can set up two equations based on the copper content and the total weight of the alloys.

Equation 1: Copper content equation The copper content in the first alloy is 40% of x kilograms, and the copper content in the second alloy is 32% of y kilograms. The copper content in the final alloy is 35% of the total weight (8 kg). Therefore, we can write the equation as:

0.4x + 0.32y = 0.35 * 8

Equation 2: Total weight equation The total weight of the alloys is 8 kg. Therefore, we can write the equation as:

x + y = 8

Now, we can solve these equations to find the values of x and y.

Solving the Equations

We can solve the equations using substitution or elimination. Let's use the substitution method.

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

x = 8 - y

Substituting this value of x into Equation 1, we get:

0.4(8 - y) + 0.32y = 0.35 * 8

Simplifying the equation:

3.2 - 0.4y + 0.32y = 2.8

Combining like terms:

-0.08y = -0.4

Dividing both sides by -0.08:

y = -0.4 / -0.08

y = 5

Substituting this value of y back into Equation 2, we get:

x + 5 = 8

Subtracting 5 from both sides:

x = 8 - 5

x = 3

Answer

To obtain an alloy weighing 8 kg with a copper content of 35%, we need to take 3 kg from the first alloy (containing 40% copper) and 5 kg from the second alloy (containing 32% copper).

Therefore, 3 kg should be taken from the first alloy and 5 kg should be taken from the second alloy to obtain the desired alloy.