SOLUTION: I started submitting a question and didnt finish so I will do it again. For the following function, C computes a value, where if you add millions of dollars to the value, the re

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I started submitting a question and didnt finish so I will do it again. For the following function, C computes a value, where if you add millions of dollars to the value, the re      Log On


   

Question 295525: I started submitting a question and didnt finish so I will do it again.
For the following function, C computes a value, where if you add millions of dollars to the value, the result is the cost of implementing a city recycling project when x as a percent(not a decimal equivalent), citizens participate
C(x)= 1.5x/100-x
a.) Using this model, determine the cost if 60% of the citizens participate?

b.)Using this model, find the percentage of participation that can be expected if $5 million is spent on this recycling project? Set up the equation and solve algebraically. Round to the nearest whole percent.
I would appreciate help on this one, I am not sure how to do it, and would love to see it step by step.
Thank you for your help
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a) Just plug in x=60 to get: C%2860%29=%281.5%2A60%29%2F%28100-60%29=90%2F40=9%2F4=2.25. So the cost is 2.25 million.

b) Since we want the cost to be 5 million, we let C%28x%29=5 and plug it in to get 5=%281.5x%29%2F%28100-x%29. Now we solve for 'x':


5=%281.5x%29%2F%28100-x%29 Start with the given equation.


5%28100-x%29=1.5x Multiply both sides by 100-x.


500-5x=1.5x Distribute.


500=1.5x%2B5x Add 5x to both sides.


500=6.5x Combine like terms.


500%2F6.5=x Divide both sides by 6.5 to isolate 'x'.


76.9230769=x Divide


Now round to the nearest whole number to get x=77


So the percentage is 77% (to the nearest whole percentage)