SOLUTION: I have two questions that have to do with the same model. For the following function, C computes the cost in millions of dollars of implementing a city recycling project when x per

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Question 122545: I have two questions that have to do with the same model. For the following function, C computes the cost in millions of dollars of implementing a city recycling project when x percent of the citizens participate.
C(x)= 1.5x/100-x
Using this model, approximately what is the cost if 60% of the citizens participate?
Using this model, estimate the percentage of participation that can be excepted if $5 million is spent on this recycling project? Set up an equation and solve algebraically. Round to the nearest whole percent.
I don't understand how to do this so any suggestions will be very helpful. Thank you
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
For the following function, C computes the cost in millions of dollars of implementing a city recycling project when x percent of the citizens participate.
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Assuming you mean:
C(x)= 1.5x%2F%28%28100-x%29%29
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Using this model, approximately what is the cost if 60% of the citizens participate?
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Just substitute 60 for x in the given equation
C(x)= 1.5%2860%29%2F%28%28100-60%29%29
C(x)= 90%2F40
C(x) = 2.25 million$
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Using this model, estimate the percentage of participation that can be excepted if $5 million is spent on this recycling project? Set up an equation and solve algebraically. Round to the nearest whole percent.
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Replace C(x) with 5, and solve for x:
5 = 1.5x%2F%28%28100-x%29%29
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Multiply both sides by (100-x) and you have:
5(100-x) = 1.5x
500 - 5x = 1.5x
500 = 1.5x + 5x; added 5x to both sides:
500 = 6.5x
x = 500/6.5
x = 77% participate when $5 million is spent
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Check solution find C(x) when x = 77%
C(x)= 1.5%2877%29%2F%28%28100-77%29%29
C(x)= 115.5%2F23
C(x)= 5.02 ~ 5; confirms our solution
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