Per capita ship 20÷4=5 (yuan).

A big ship is cheaper than a small one. If a small boat can't be full, rent as many big boats as possible.

45-6×7=3 people, and the remaining 3 people rent a boat.

Rent 6 big boats, 1 small boat.

6×28+20= 188 (yuan)

This is that most economical method.

If two teachers also want to take a boat, then

47-5×7= 12 (person)

12÷4=3 (only)

Rent five big boats and three small boats.

5×28+3×20=200 (yuan)