Consider a cost-benefit model is y=2694x/100-x, where y is the the cost for removing x percent of a given pollutant. What percent can be removed for $33,000?
The answer given to me as 92.5% but dont know how to sove it

Question

Consider a cost-benefit model is y=2694x/100-x, where y is the the cost for removing x percent of a given pollutant. What percent can be removed for $33,000?
 The answer given to me as 92.5% but dont know how to sove it

anonymous · Answer

Substitute 33,000 in for y, can you proceed from here:
$$33000 = 2694x / 100 - x$$

anonymous · Answer

When I plug in 92.5% for  x, which was the answer given to me by my professor it doesn't give me $33,000 it gives me 33,226. The 100-x was throwing me off too. not sure where to start

anonymous · Answer

That's due to the round off error.

anonymous · Answer

The precise answer is 92.45251303 percent. It's probably more precise than that, but when you plug that into a formula with large numbers (Such as 3 million), the error propagation gets large....

gw2011 · Answer

Maybe this might help.  The original equation shown by qpHalcynOn as:

2694x/(100-x)=33,000 is correct

Now multiply both sides of the equation by (100-x) in order to get rid of the fraction and you get:

2694x=33,000(100-x)
2694x=3,300,000-33,000x
2694x+33,000x=3,300,000
35,694x=3,300,000
x=92.45%= approximately 92.5%  (This is rounded)

anonymous · Answer

thank you :)

gw2011 · Answer

You're welcome.