SOLUTION: 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)= 1.4X/100-X

Question 112416: 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)= 1.4X/100-X (that is 1.4x divided by 100-x)
a) Using this model, approximately what is the cost if 60% of the citizens participate?

b) Using this model, estimate the percentage of participation that can be excepted if $4 million is spent on this recycling project. Set up an equation and solve algebraically. Round to the nearest whole percent.

Answer by uma(370) (Show Source): You can put this solution on YOUR website!
When x% of the citizens participate then the cost is:
C = 1.4x/ (100 - x)
When 60% of citizens participate,
C = 1.4*60/(100-60)
= 84/40
= 2.1
Thus if 60% participate the cost is $2.1 million.
(b) Let x be the % od participation
Then 1.4x/ (100 - x) = 4
==> 1.4x = 4(100 - x)
==> 1.4x = 400 - 4x
==> 1.4x + 4x = 400
==> 5.4x = 400
==> x = 400/5.4
==> x = 74.074
Thus if $4 millions is spent then approx 74% of the citizens must have participated.

Good luck!!!

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