Can someone help me with this.....?

Question

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)

a.) Using this model, approximately what is the cost if 40% of the citizens participate?

b) 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.

Answer 1

C(x)=(1.5x/100-x)
if we let x = 40%:
C(x) = (1.5(40)/100-40)
C(x)=60/60 = 1
so 1 million dollars if 40% participates

Now they want to know what percent has to participate if the cost is $5 million, so work backwards:

C(x)=(1.5x/100-x)
5 = 1.5x / 100 - x
solve for x
5(100-x) = 1.5x
500 - 5x = 1.5x
500 = 1.5x + 5x
500 = 6.5x
76.9 =x
so 76.9%, or 77%, rounding to nearest percent.

Answer 2

I assume you mistyped the function and you really mean: C(x) = (1.5x)/(100-x)

a.) set x=40 and solve for C(40):

C(40) = (1.5*40/100-40) = 60/60= 1

answer is $1 million

b.) set C(x)=5 and solve for x:

C(x) = 5 = (1.5x)/(100-x) ...... 5(100-x) = 1.5x ......
500 - 5x = 1.5x ....... 500 = 6.5x ...... x = 500/6.5 .....
x = 76.923

with rounding, x = 77, so the estimated participation is 77%

Answer 3

C(x) ) = 1.5x/(100-x) I think the brackets are missing

pick x=40% C(40) = 1.5*40/60 = 1 million

C(x) = 5 = 1.5x/(100-x)
1.5x = 5 (100-x) = 500 -5x
6.5x = 500
x =500/6.5 = 76.923%

Answer 4

a) Plug in 40 for x: C=(1.5*40/(100-40))=1 (million)

b) Solve for x: C=1.5x/(100-x) => 100C-Cx=1.5x => 100C=1.5x+Cx => 100C/(1.5+C) = x
Plug in 5 for C: 100*5/(1.5+5) = 77 (%)