Lottery Problem: shares cut by $75K when 3 more winners show

[medas]

Some people come forward to claim a $1,000,000 lottery jackpot, which the winners are to share equally. Before the jackpot is divided, three more winning ticket holders show up. As a result, each person's share is reduced by $75,000. How many winners are there and what were their shares?

100000/x) - 75000 = 100,000/(n+3) is this right?

similar problem or how to set-up

 

[arthur ohlsten]

Re: Lottery Problem? confuse

assume n people won
Each won 1,000,000 / n=W1

assume n+3 people won
each won 1,000,000 / [n+3]=W2

but W2 = W1 - 75,000
substitute
1,000,000/[n+3] = 1,000,000/n -75000

multiply by [n][n+3]
1,000,000 n= 1,000,000[n+3] - 75,000 n[n+3]
0=3,000,000 -75,000n^2 - 225,000n
75 n^2+ 225 n -3,000 =0
3n^2 + 9 n -120=0
n^2+3n-40=0
n=-3+/- [9 +160]^1/2 all over 2
n=-3/2 +/- 13/2
n=-16/2 extraneous solution or n=10/2

each thought they won 200/000
they actually won 125,000

Arthur