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?

1 answer

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.
Similar Questions
  1. The labor movement quizWhat negative impact in gold and silver mine and have on the west tent cities near the mines florist in
    1. answers icon 1 answer
  2. What negative impact did gold and silver mining have on the west?1. Tent cities near the mines faster terminal is long-term
    1. answers icon 1 answer
  3. How can bats benefit from mining?Question 2 options: Underground mines that are left open may become homes for bats Insects are
    1. answers icon 1 answer
  4. Which best states the central claim in the passage?Responses A Professor Williams grew up in coal-mining country.Professor
    1. answers icon 1 answer
more similar questions