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# Function help

A cost-benefit function C computes the cost, in millions of dollars, of implementing a city recycling project where x percent of the citizens participate, where. C(x)=x/100-x

a) If 75 percent participation is expected, determine the cost for the city recycling project.

b) The city plans to spend \$5 million on this project. Estimate the percentage of participation that can be expected.

### 1 Answer by Expert Tutors

Erik D. | High School and Undergraduate Mathematics TutorHigh School and Undergraduate Mathematic...
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If x refers to the percent then x=75.
a. An important note to make here is that the functions should read C(x)= x/(100-x) otherwise a negative result would occur and that doesn't make sense in the context of the question.
with x=75,
C(75)=75/(100-75)=75/25=3
where 3 is in millions of dollars.
b. the cost is 5 million dollars and C(x) is in millions of dollars so C(x)=5.
C(x)=5=x/(100-x)
5(100-x)=x by multiplying each side by (100-x)
500-5x=x by distributing the 5 to each term
500=6x by adding 5x to both sides
500/6=x by dividing 6 by both sides
83.33=x (approximately) where x is the percentage of citizens who participated.