Question

Є два сплави міді й олова; перший містить 40% міді, а другий - 60%. Скільки потрібно взяти кожного сплаву, щоб одержати 10кг нового сплаву, який би містив 54% міді?

Answer 1

Пусть нужно взять х кг первого сплава, тогда второго сплава нужно взять 10-х кг, составим уравнение:

х*40/100+(10-х)*60/100=10*54/100

0,4х+6-0,6х=5,4

6-5,4=0,6х-0,4х

0,6=0,2х

х=0,6:0,2

х=3 (кг) - нужно взять первого сплава

10-3=7 (кг) - нужно взять второго сплава

Answer 2

Problem Analysis

We have two alloys, one containing 40% copper and the other containing 60% copper. We need to determine how much of each alloy should be taken to obtain a new alloy weighing 10kg and containing 54% copper.

Solution

Let's assume we take x kg of the alloy with 40% copper and y kg of the alloy with 60% copper.

To find the amount of copper in the new alloy, we can use the following equation:

0.4x + 0.6y = 0.54 * 10

Simplifying the equation, we get:

0.4x + 0.6y = 5.4

Now we have a system of two equations:

x + y = 10 (since the total weight of the new alloy is 10kg) 0.4x + 0.6y = 5.4 (equation representing the copper content)

We can solve this system of equations to find the values of x and y.

Solving the System of Equations

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

Multiplying the first equation by 0.4, we get:

0.4x + 0.4y = 4

Subtracting this equation from the second equation, we eliminate x:

(0.4x + 0.6y) - (0.4x + 0.4y) = 5.4 - 4

0.2y = 1.4

Dividing both sides by 0.2, we find:

y = 1.4 / 0.2

y = 7

Substituting the value of y back into the first equation, we can find x:

x + 7 = 10

x = 10 - 7

x = 3

Therefore, we need to take 3kg of the alloy with 40% copper and 7kg of the alloy with 60% copper to obtain a new alloy weighing 10kg and containing 54% copper.

Answer

To obtain a new alloy weighing 10kg and containing 54% copper, you need to take 3kg of the alloy with 40% copper and 7kg of the alloy with 60% copper.