Answer
The year in which the violent crime incidents decrease to $289$ per 100,000 people is $2019$.
Work Step by Step
Consider the number of years after the year $1994$ to be $x$.
The violent crime incidents per 100,000 Americans in the year $1994$ is $714$.
Then, the decrease in violent crime incidents per 100,000 people from year $1994$ to 2014 is $17x$.
Write the equation, which describes that the decrease in violent crime from $714$ to $17x$ is equal to $289$ per 100,000 people.
$714-17x=289$
Subtract $289$ from both sides and add $17x$ on both sides.
$\begin{align}
& 714-17x-289+17x=289-289+17x \\
& 425=17x
\end{align}$
Divide both sides by $17$.
$\begin{align}
& \frac{425}{17}=\frac{17x}{17} \\
& 25=x
\end{align}$
The number of years after $1994$ is $25$. So, the year is,
$\begin{align}
& 1994+x=1994+25 \\
& =2019
\end{align}$
Therefore, the year in which the violent crime incidents decreases to $289$ per 100,000 people is $2019$.
