6. A real estate agent is trying to sell the last apartment in a building for $482,100 \mathrm{kn}$, which was the price of the penultimate apartment, and by doing so, the average price of the apartments he sold in that building would be $519,500 \mathrm{kn}$. However, due to market saturation, he sells the apartment for only $451,500 \mathrm{kn}$, making the average price of the apartments he sold in that building $517,700 \mathrm{kn}$. How many apartments in that building has the real estate agent sold?
6. Let $n$ be the number of apartments sold by the real estate agent, and

$$
\begin{array}{cc}
x_{1}, x_{2}, \ldots, x_{n-1} \text { prices of previously sold apartments. } & 1 \text{ POINT} \\
\text { Then } \frac{x_{1}+x_{2}+\ldots+x_{n-1}+482100}{n}=519500 & 1 \text{ POINT} \\
\text { and } \frac{x_{1}+x_{2}+\ldots+x_{n-1}+451500}{n}=517700 & 1 \text{ POINT}
\end{array}
$$

Further, $x_{1}+x_{2}+\ldots+x_{n-1}+482100=519500 n \quad 1$ POINT

and $x_{1}+x_{2}+\ldots+x_{n-1}+451500=517700 n . \quad 1$ POINT

It follows that $30600=1800 n \quad 3$ POINTS

or $n=17$. 1 POINT

The real estate agent sold 17 apartments in that building. 1 POINT

TOTAL 10 POINTS