Solve the problem.
-Suppose a cost-benefit model is given by $y = \frac { 2974 x } { 100 - x }$, where $y$ is the cost for removing $x$ percent of a given pollutant. What percent of pollutant can be removed for $\$ 30,000$ ? Round your answer to the nearest tenth of a percent.
A) $91.0 \%$
B) $111.0 \%$
C) $9.1 \%$
D) $502.2 \%$

Question

Quizplus · Accepted Answer

To find the percent of pollutant that can be removed for $30,000, we need to set the given equation equal to $30,000 and solve for x:
\begin{align*}
30,000 &= \frac{2974x}{100-x}\
30,000(100-x) &= 2974x\
3,000,000-30,000x &= 2974x\
33074x &= 3,000,000\
x &= \frac{3,000,000}{33074} \approx 90.95\%
\end{align*}
Rounded to the nearest tenth, we get 91.0%. Therefore, the answer is A.

Solve the Problem y=2974x100−xy = \frac { 2974 x } { 100 - x }y=100−x2974x​

Solve the Problem $y = \frac { 2974 x } { 100 - x }$