The 20 original trailers are now an average of 20 years old, and the \(n\) new trailers are all 2 years old. There are \(20+n\) trailers, and the sum of their ages is \(20\cdot20+2n\). This gives us the equation
\(\frac{400+2n}{20+n}=14, \)
which we solve like this:
\(\begin{align*} 400+2n &= 14(20+n) \\ 400+2n &= 280+14n \\ 120 &= 12n \end{align*}\)
We find that there are \(n=10\) new trailer homes.
(Source: AoPS Alcumus)
