Chapter 9.4, Problem 29P

A flock of geese on a pond was being observed continuously. At 1:00 P.M., $\frac{1}{5}$ of the geese flew away. At 2:00 P.M., $\frac{1}{8}$ of the geese that remained flew away. At 3:00 P.M., 3 times as many geese flew away as had flown away at 1:00 P.M., leaving 28 geese on the pond. At no other time did any geese arrive or fly away. How many geese were in the original flock? Solve this problem, and explain your solution.