Let $n$ is number of frogs that are not among $50$ lightest and $44$ heaviest. There $43\%$ such frogs We have $\frac{30}{50} \leq \frac{43}{n} \leq\frac{27}{44} \to n=71$ and total $50+71+44=165$ frogs

RagvaloD wrote: Let $n$ is number of frogs that are not among $50$ lightest and $44$ heaviest. There $43\%$ such frogs We have $\frac{30}{50} \leq \frac{43}{n} \leq\frac{27}{44} \to n=71$ and total $50+71+44=165$ frogs I believe you've forgotten to show that no solutions exist for the case where the $50$ lightest frogs contains some of the $44$ heaviest frogs?