The ratio of police detectives and private detectives on the island is 6 to 5. If a total of 550 detectives of both kinds live on the island, how many are POLICE detectives?
The total number of ratio units in 6:5 is 6+5=11, so each of those ratio units must stand for 550/11 = 50 detectives. Then the 6 ratio units of police detectives stand for 6·50 = 300 police detectives.
