Three flocks

Flocks of birds pass by, and one bird on a tree asks them, how many of you? And they respond, we are so plenty. The second flock of birds again passes by and asks the bird on a tree, how many of you? The response is we are one-half (1/2) of the first flock of birds. The third flock passes by and asks once again by the bird on a tree, how many of you? The response is that we are one-third (1/3) of the first flock, but if you go with us, we are all one hundred.
Question?
1.) how many birds are there in the first flock?
2.) how many birds are in the second flock?
3.) how many birds are there in the third flocks?

Correct answer:

a =  54
b =  27
c =  18

Step-by-step explanation:

$$\begin{gathered} a+a/2+a/3<100 \\ 6a+3a+2a<600 \\ 11a<600 \\ a=\lfloor 600/11\rfloor =54 \end{gathered}$$

$b=a/2=54/2=27$

$$\begin{gathered} c=a/3=54/3=18 \\ \text{ Verifying Solution: } \\ s=a+b+c=54+27+18=99 \end{gathered}$$

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