The cost C, in dollars, to remove p percent of a certain pollutant fro

required cost = (100,000 * 90)/(100 - 90) - (100,000 * 80) /(100 - 80)
= 100,000 * (90/10 - 80/20)
= 100,000 * (9 - 4)
= 100,000 * (5)
= 500,000

answer choice A

The cost to remove 90 percent of the pollutant is determined by letting p = 90 in the cost formula:

100,000(90)/(100 – 90) = 9,000,000/10 = 900,000

Similarly, the cost to remove 80 percent of the pollutant is determined by letting p = 80 in the cost formula:

100,000(80)/(100 – 80) = 8,000,000/20 = 400,000

To determine how much more it costs to remove 90 percent of the pollutant than 80 percent of the pollutant, we calculate the difference of the two costs:

900,000 – 400,000 = 500,000

Answer: A

Attached is a visual that should help. In order to solve this question correctly, you must realize that p is expressed as a percent and thus should not be converted to a decimal.

After checking the solution for this exercise, it looks quite easy. I just don't understand one thing. Why can I just plug the 90 and the 80 for p in the formula and not 90% (90/100) or 80% (80/100)?

i.e.: 100,000(90/100) / 100 - (90/100)

Thanks a lot.

Hi Bunuel ,

Why not just plug in the difference (10%) into the equation? That's what I did first but I got a wrong answer. I read Hero8888 's explanation but I don't understand.

How come getting the percent difference here will not work? For me it seems logically sound. Where does this logic go wrong here?

Thanks.

Hi - the only way plugging in 10 % (difference between 90 and 80) will work is if the variable x is attached to ALL elements of the equation ...example below

A) 10 x - (4/5) x --> if you plug in 90 and 80 separately and subtract or just plug in 10 %, you will get the same answer
B) 18x + 5x ------> if you plug in 90 and 80 separately and subtract or just plug in 10 %, you will get the same answer
C) 10 x - 6x --------> if you plug in 90 and 80 separately and subtract or just plug in 10 %, you will get the same answer
D) 125 x / 6 --------> if you plug in 90 and 80 separately and subtract or just plug in 10 %, you will get the same answer

However If you have the following equation where X is not attached to the constant -- plugging in 10 % will fail
example : 100 + (x) --> if you plug in 90 and 80 separately and subtract or just plug in 10 , you will get DIFFERENT answers

Logic : when you are subtracting (90 - 80) to give you 10 % --> you are getting rid of the constant within the equation (in above case, 100 in blue color) ..when you plug in 10 %, the constant remains...

In this equation, the numerator has the x attached to it, but the 100 underline does not and thus will fail if you put in just a 10
I) 100,000 * X / (100-X)

Don't we think that 90 percent means \(\frac{90}{100}=0.90\)?

Hope help from you.

Solution:

“90 percent” indeed means 90/100 = 0.9; however, we can’t replace p by “90/100”” or “0.9”, each of which is equivalent to “90 percent.” Recall that the sentence describing the formula is “The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C = 100,000p/(100 - p)”. From the wording of the sentence, we see that “p percent” requires that p be the actual percent value, not its decimal or fractional equivalent.

Answer: Option A

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­I still don't get it, please help?

Can someone please explain why are we not taking 90/100?

 
­
Check the question:
­As you can see, the stem mentions "p percent" and then inquires about "90 percent" and "80 percent." Simply substitute p with 90 and 80 to obtain p = 90 and p = 80.

Hope it helps.

­Thanks for the response! I understand now.

­Does it also apply for "%" symbol too? 

Yes, the "%" symbol and the word "percent" mean the same thing, so they are used interchangeably.

­Hi why didnt we take it as 0.9 as the question mentioned p as percent?