There are 50 students in an auditorium, of which 2x are boys and y are girls. After (y - 6) boys leave the auditorium and (2x - 5) girls enter the auditorium, the probability of selecting a girl at random becomes 9/13. Find the value of x and of y?
Total number of students=50 Number of boys=2x Number of girls=y total will be: 2x+y=50 ⇒y=50-2x
when (y-6) boys left the auditorium the new number of boys was: 2x-(y-6) =2x-y+6 but y=50-2x thus the new number will be: 2x-(50-2x)+6 =4x-44
when (2x-5) girls left the auditorium the remaining number will be: y-(2x-5) =y-2x+5 but y=50-2x thus the new number of girls will be: 50-2x-2x+5 =55-4x new total number of students: (55-4x)+(4x-44) =11
probability of selecting a girl at random will be: (55-4x)/11=9/13 13(55-4x)=9*11 715-52x=99 616=52x x=12 thus y=50-12=38 thus x=12 and y=38
