Answer
$15$ years.
Work Step by Step
Let the number of crossing $=x$.
Toll to a bridge costs $=\$8$.
Total costs for crossing $x$ times $=8t$.
Monthly discount pass $=\$45$.
With discount the toll is $\$5$.
Total costs for crossing $x$ times $=45+5t$.
Equate both total costs to find the number of crossing for which both are same.
$\Rightarrow 8t=45+5t$
Subtract $5t$ from both sides.
$\Rightarrow 8t-5t=45+5t-5t$
Simplify.
$\Rightarrow 3t=45$
Divide both sides by $3$.
$\Rightarrow \frac{3t}{3}=\frac{45}{3}$
Simplify.
$\Rightarrow t=15$
Hence, after $15$ years both total costs are equal.
