3. At a congress, all attendees are either mathematicians or biologists, and no one is both a mathematician and a biologist. The mathematicians all know each other and each knows four of the biologists. The biologists all know each other and each knows nine of the mathematicians. It turns out that every mathematician knows exactly twice as many people as every biologist. (If person A knows person B, then person B also knows person A.)

How many mathematicians are there at the congress?