Hard math question

Question

Two Type of players came to a chess club
weak and strong.There were 10 more strong players than the weak.All strong players played against all strong players and all weak players played against all weak players.The amount of games played was 2005. How many strong and weak players played?

Answer 1

Add,

 

Let there be w weak players

 

So strong players = w + 10

 

Number of all the games played by weak players = w!/((w-2)!*2!) = w*(w-1)/2

 

Number of all the games played by strong players = (w+10)!/((w+8)!*2!) = (w+10)(w+9)/2

 

Total games = w*(w-1)/2 + (w+10)(w+9)/2 = 2005

 

w(w-1) + (w+10)(w+9) = 4010

w^2 -w + w^2 +19w +90 -4010 = 0

2w^2 + 18w -3920 = 0

 

w^2 + 9w -1960 = 0

w^2 + 49 w -40 w -1960 = 0

w(w+49) -40 (w + 49) = 0

(w-40)(w+49) = 0

 

w = 40

 

So there are 40 weak players and 50 strong players

Answer 2

Look at Sanjay's solution while I check mine. I misunderstood the question.