Answer
after \[40\]years, the average ticket of the movie ticket will be \[\$8.69\].
Work Step by Step
Consider the ticket price in \[1980\], which is \[\$2.69\] and the ticket price increased at a rate \[\$0.15\]per year. So, take\[x\] as a year, then ticket price will be\[\$0.15x\]. To get the year in which the average price of the movie ticket will be\[\$8.69\], then governing equation form as:
\[\begin{align}
& 0.15x+2.69=8.69 \\
& 0.15x=8.69-2.69 \\
& 0.15x=6 \\
& x=\frac{6}{0.15}
\end{align}\]
Further,
\[\begin{align}
& x=\frac{6}{0.15} \\
& =\frac{600}{15} \\
& =40
\end{align}\]
So, after \[40\]years, the average ticket of the movie ticket will be \[\$8.69\].
