Answer
$187,239 \text{ tons}$
Work Step by Step
The variation model described by the problem is $
P=kN
,$ where $P$ is the amount of pollution and $N$ is the population.
Substituting the given values in the variation model above results to
\begin{array}{l}\require{cancel}
270000=k(460000)
\\\\
\dfrac{270000}{460000}=k
\\\\
k=\dfrac{27}{46}
.\end{array}
Therefore, the variation equation is $
P=\dfrac{27}{46}N
.$
Using the variation equation above, then
\begin{array}{l}\require{cancel}
P=\dfrac{27}{46}(319000)
\\\\
P=187239.13043478260869565217391304
.\end{array}
Rounded to the nearest whole ton, the number of tons of pollution is $
187,239 \text{ tons}
.$
