A biologist found a pond with frogs. When classifying them by their mass, he noticed the following:

The $50$ lightest frogs represented $30\%$ of the total mass of all the frogs in the pond, while the $44$ heaviest frogs represented $27\%$ of the total mass.

As fate would have it, the frogs escaped and the biologist only has the above information. How many frogs were in the pond?

Let's think step by step and output the final answer within \boxed{}.
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