Suppose a cost-benefit model is given by y=2771x/100-x, where y is the cost for removing x percent of a given pollutant. What percent of pollutant can be removed for $36,000? Round your answer to the nearest tenth of a percent?
To find the percent of pollutant that can be removed for $36,000 using the given cost-benefit model, we need to solve the equation y = 2771x / (100 - x) for x when y = $36,000.
First, substitute y = $36,000 into the equation:
$36,000 = 2771x / (100 - x)
Next, multiply both sides of the equation by (100 - x) to get rid of the denominator:
$36,000(100 - x) = 2771x
Expand the equation:
$3,600,000 - $36,000x = 2771x
Now, combine like terms:
3,600,000 = 2771x + $36,000x
3,600,000 = 3137x
Divide both sides of the equation by 3137:
x = 3,600,000 / 3137
This gives us the value of x, which represents the percentage of the pollutant that can be removed for $36,000.
Now, calculate the value of x using a calculator or doing the division manually:
x ≈ 1147.004
Rounded to the nearest tenth of a percent, the percentage of pollutant that can be removed for $36,000 is approximately 1147 percent.
To find the percent of pollutant that can be removed for $36,000, we need to solve the cost-benefit equation y = 2771x / (100 - x) for x.
Given y = $36,000, the equation becomes:
36000 = 2771x / (100 - x)
To solve for x, we first multiply both sides of the equation by (100 - x):
36000(100 - x) = 2771x
Expanding the equation:
3600000 - 36000x = 2771x
Next, we move all the x terms to one side of the equation:
36000x + 2771x = 3600000
Combine like terms:
38771x = 3600000
To isolate x, we divide both sides of the equation by 38771:
x = 3600000 / 38771
Calculating x:
x ≈ 92.9
Therefore, approximately 92.9% of the pollutant can be removed for $36,000, rounded to the nearest tenth of a percent.
just solve for x in
2771x/(100-x) = 36000
x = 92.85%