Answer
The total costs for solar heating and electric heating will be the same in 26 years and the cost at that year is $\$33,600$.
Work Step by Step
Let $x$ be the year at which the total costs for solar heating and electric heating will be the same.
Therefore,
$\begin{align}
& 29700+150x=5000+1100x \\
& 1100x-150x=29700-5000 \\
& 950x=24700 \\
& x=\frac{24700}{950}
\end{align}$
Further simplified,
$x=26$
Now, the cost at 26 years is
$\begin{align}
& 29700+150\left( 26 \right)=29700+3900 \\
& =33600
\end{align}$
Hence, the total costs for solar heating and electric heating will be the same in 26 years and the cost at that year is $\$33,600$.
