Question

The ratio of males to females in a room is 5 to 4. If 5 males and 6 females leave the room, the ratio of m to f becomes 4 to3. How many people were in the room originally

Answer 1

Let f and m be the number of females and males in the room prior to anyone leaving the room, respectively. Solve the following simultaneous equations for m and f.\[\frac{m}{f}=\frac{5}{4},\frac{m-5}{f-6}=\frac{4}{3}\]{m = 45, f = 36}