15. (15 points) A bag of balls, with red and yellow colors, first 60 balls are taken out, among which there are exactly 56 red balls. Afterwards, each time 18 balls are taken out, there are always 14 red balls, until the last 18 balls are exactly taken out. If the total number of red balls in this pile is exactly four-fifths of the total number of balls, how many red balls are there in the bag?
【Solution】Solution: Let the number of times be $x$, then the total number of balls is $60+18 x$, and the number of red balls is $56+14 x$. According to the problem, we have:
$$
\begin{array}{l}
(56+14 x) \div(60+18 x)=\frac{4}{5}, \\
56+14 x=(60+18 x) \times \frac{4}{5}, \\
56+14 x=48+14.4 x, \\
0.4 x=8, \\
x=20, \\
56+14 \times 20=336 \text { (balls); }
\end{array}
$$

Answer: There are a total of 336 red balls in the bag.