the function 160x/100-x,models the cost,f(x), in millions of dollars,to remove x% of a river pollutants,if the government commits 240 million for this project, what percentage of pollutants can be removed?
well, just solve
160x/(100-x) = 240
160x = 24000 - 240x
400x = 24000
x = 60
Let's start by setting up the equation based on the given information.
The cost function is given as f(x) = (160x) / (100 - x), where x represents the percentage of pollutants to be removed.
We are given that the government commits 240 million dollars for this project, so we can set up an equation:
240 = (160x) / (100 - x)
To solve for x, we can cross-multiply:
240(100 - x) = 160x
Expanding the equation:
24000 - 240x = 160x
Combining like terms:
24000 = 400x
Divide both sides by 400:
60 = x
So, the percentage of pollutants that can be removed is 60%.
To find the percentage of pollutants that can be removed, we need to solve the equation f(x) = 240 million and find the value of x.
The given function is f(x) = 160x / (100 - x), where f(x) represents the cost in millions of dollars to remove x% of the pollutants.
So, we have the equation:
240 = 160x / (100 - x)
To solve for x, we can start by multiplying both sides of the equation by (100 - x) to get rid of the denominator:
240 * (100 - x) = 160x
Expanding the equation, we get:
24000 - 240x = 160x
Combining like terms:
24000 = 400x
Now, we can solve for x by dividing both sides of the equation by 400:
x = 24000 / 400
x = 60
Therefore, the percentage of pollutants that can be removed is 60%.