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Nice one — this simplifies neatly.

Let = number of girls, boys.
Swimmers .
Runners .
Everyone chose at least one, so .

Compute:

\begin{aligned}
\text{both} &= (0.8G+0.5B)+(0.6G+0.7B)-250 \\
&=1.4G+1.2B-250 \\
&=1.4G+1.2(250-G)-250 \\
&=50+0.2G = 50+\frac{G}{5}.
\end{aligned}

Given is between and of 250, i.e. .
So

Minimum when : both .

Maximum when : both .


Answer: minimum 72, maximum 80 students.

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