13.067. On the first day of the sports competitions, $1 / 6$ of the boys' team and $1 / 7$ of the girls' team did not meet the qualifying standards and were eliminated from further competition. Over the rest of the competition period, an equal number of athletes dropped out from both teams due to failing to meet the standards. By the end of the competition, a total of 48 boys and 50 girls did not meet the qualifying standards, but among those who did meet the standards, the number of girls was twice that of the boys. What was the initial number of athletes in each team?
## Solution:

Let $x$ be the number of boys who met the credit standards and $2x$ be the number of girls. Then the initial number of team members is $x+48$ boys and $2x+50$ girls. By the end of the first day of the competition, $\frac{1}{6}(x+48)$ boys and $\frac{1}{7}(2x+50)$ girls dropped out. Later, an equal number of athletes dropped out from both teams, so $48-\frac{1}{6}(x+48)=50-\frac{1}{7}(2x+50)$, from which $x=24$. Therefore, the initial number of team members is 72 boys and 98 girls.

Answer: 72 boys and 98 girls.