SOLUTION: One week a syndicate of x people won $1000 in a lottery. If there had been two fewer people in the syndicate, each person would have received $25 more. How many people are in the

Algebra ->  Equations -> SOLUTION: One week a syndicate of x people won $1000 in a lottery. If there had been two fewer people in the syndicate, each person would have received $25 more. How many people are in the       Log On


   

Question 1086339: One week a syndicate of x people won $1000 in a lottery. If there had been two fewer people in the syndicate, each person would have received $25 more. How many people are in the syndicate?
Found 2 solutions by Fombitz, youngalabama:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So they won, A=1000%2Fx each.
If there were 2 fewer,
1000%2F%28x-2%29=A%2B25
1000%2F%28x-2%29=1000%2Fx%2B25
1000x=1000%28x-2%29%2B25x%28x-2%29
1000x=1000x-2000%2B25x%5E2-50x
25x%5E2-50x-2000=0
x%5E2-2x-80=0
%28x-10%29%28x%2B8%29=0
Only positive x values make sense in this problem,
x-10=0
x=10
.
.
.
10 people all together.

Answer by youngalabama(1) About Me  (Show Source):
You can put this solution on YOUR website!
y = total prize
y = 1025(x-2)
1000x = y
1000x = 1025(x-2)
1000x = 1025x - 2050
-25x = 2050
x = 82