SOLUTION: If 8 boys went to the washroom, there would be 2/3 as many boys as girls in the room. If 8 girls went to the washroom, there would be 2 times as many boys as girls. How many boys a

b = number of boys

g = number of girls



b-8 = (2/3)g   (1)

2(g-8) = b     (2)



Substitute LHS of (2) for 'b' in (1):

2(g-8)-8 = (2/3)g

2g-24 = (2/3)g

6g-72 = 2g

   4g = 72  

    g = 18  -->(using (1) or (2))-->  b = 20



There are 20 boys and 18 girls in the class



Check:  

20 - 8 = 12 and 12 = (2/3)18   ((1) checks out)

2(18-8) = 2(10) = 20 = b       ((2) checks out)