Work backwards bro. To find out the afternoon competitors, we must subtract the 17 new guys who entered which leaves you with 33 people. And understand that this is 1/3 of afternoon competitors as a result of 2/3 leaving the field. So by multiplying by 3 we are able to get the total amount of afternoon people which is 99.
For the morning portion, we must subtract the 15 that came in which gives us 84. The question states that 2/9 had left. This leaves us with 7/9 left which is 84. So by dividing 84 with 7/9 we get 108. Hope that helps!