# Solve for x: A soccer club runs a raffle each week with a prize fund of \$900. In the first week, the prize was shared equally among xpeople. In the second, the prize fund was shared equally among (x - 2) people and each person received \$15 more than the winners on the first week. The soccer club runs a raffle each week with a prize fund of \$900. In the first week, the prize is equally shared between x people. Each person gets a prize of `900/x` . In the second week the prize is shared equally among x - 2 people. Each person gets...

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

The soccer club runs a raffle each week with a prize fund of \$900. In the first week, the prize is equally shared between x people. Each person gets a prize of `900/x` . In the second week the prize is shared equally among x - 2 people. Each person gets a prize of `900/(x - 2)` . As each person in week 2 received \$15 more than the amount received by each of the winners in the first week: `900/x + 15 = 900/(x - 2)`

`900/x + 15 = 900/(x - 2)`

=> (900 + 15x)(x - 2) = 900x

=> 900x + 15x^2 - 1800 - 30x = 900x

=>15x^2 - 30x - 1800 = 0

=> x^2 - 2x - 120 = 0

=> (x - 12)(x + 10) = 0

=> x = 12 and x = -10

Eliminate the neagtive root.

The value of x = 12.

Approved by eNotes Editorial Team