Question

A mining company extracts ore in two mines. In mine A it contains 1%
nickel and 2% copper; in mine B it is 2% nickel and 5% copper.

How much should we extract from each mine to obtain 4 tons of nickel?

and 9 copper?

Answer 1

To calculate the amount of ore to extract from each mine, we can set up a system of equations.

Let's assume x represents the amount of ore (in tons) to extract from mine A and y represents the amount of ore (in tons) to extract from mine B.

From the problem, we know that:
- In mine A, 1% of the ore is nickel. Therefore, the amount of nickel obtained from mine A is 0.01x tons.
- In mine B, 2% of the ore is nickel. Therefore, the amount of nickel obtained from mine B is 0.02y tons.

We want to obtain 4 tons of nickel in total. So, we can set up the equation:
0.01x + 0.02y = 4

Similarly, we can set up an equation for the amount of copper obtained:
- In mine A, 2% of the ore is copper. Therefore, the amount of copper obtained from mine A is 0.02x tons.
- In mine B, 5% of the ore is copper. Therefore, the amount of copper obtained from mine B is 0.05y tons.

We want to obtain 9 tons of copper in total. So, we can set up the equation:
0.02x + 0.05y = 9

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

Multiplying the first equation by 100 to eliminate decimals, we get:
x + 2y = 400 (Equation 1)

Multiplying the second equation by 100 to eliminate decimals, we get:
2x + 5y = 900 (Equation 2)

Multiply Equation 1 by 2:
2x + 4y = 800 (Equation 3)

Subtract Equation 3 from Equation 2:
2x + 5y - (2x + 4y) = 900 - 800
y = 100

Substitute y = 100 into Equation 1:
x + 2(100) = 400
x + 200 = 400
x = 200

Therefore, we should extract 200 tons of ore from mine A and 100 tons of ore from mine B to obtain 4 tons of nickel and 9 tons of copper.