The cost \(C,\) in dollars, to remove \(p\) percent of a certain pollutant from a pond is estimated by using the formula \(C = \dfrac{100,000p}{100 - p}.\) According to this estimate, how much more would it cost to remove \(90\) percent of the pollutant from the pond than it would cost to remove \(80\) percent of the pollutant?
(A) \(\$500,000\)
(B) \(\$100,000\)
(C) \(\$50,000\)
(D) \(\$10,000\)
(E) \(\$5,000\)
Answer: A
Source: Official Guide
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The cost \(C,\) in dollars, to remove \(p\) percent of a certain pollutant from a pond is estimated by using the formula
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Solution:Vincen wrote: ↑Thu Jan 14, 2021 12:22 pmThe cost \(C,\) in dollars, to remove \(p\) percent of a certain pollutant from a pond is estimated by using the formula \(C = \dfrac{100,000p}{100 - p}.\) According to this estimate, how much more would it cost to remove \(90\) percent of the pollutant from the pond than it would cost to remove \(80\) percent of the pollutant?
(A) \(\$500,000\)
(B) \(\$100,000\)
(C) \(\$50,000\)
(D) \(\$10,000\)
(E) \(\$5,000\)
Answer: A
Source: Official Guide
The cost of removing 90 percent of the pollutant from the pond is C = 100,000(90) / (100 - 90) = 900,000 dollars. Similarly, the cost of removing 80 percent of the pollutant from the pond is C = 100,000(80) / (100 - 80) = 400,000 dollars. Thus, the difference between the costs of removing 90% and 80% of the pollutant from the pond is 900,000 - 400,000 = 500,000 dollars.
Answer: A
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