alegbra

• Jan 20th 2008, 07:51 AM
Niamh Dixon
alegbra
How do you do the following question
In a draw winners shared equally in a prize of 120 euro. If there had been 3 more winners then each winner would have received 9 euro less.
Taking x as the actual number of winners, write an equation in x to represent the above information.
Solve the equation to find the actual number of winners and the amount each received.
• Jan 20th 2008, 08:04 AM
Soroban
Hello, Niamh Dixon!

Quote:

In a draw, winners shared equally in a prize of 120 euro.
If there had been 3 more winners then each winner would have received 9 euro less.
Taking $\displaystyle x$ as the actual number of winners, write an equation in $\displaystyle x$
to represent the above information.
Solve the equation to find the actual number of winners and the amount each received.

Let $\displaystyle x$ = number of winners.

They would each get $\displaystyle \frac{120}{x}$ euro. .[1]

If there were 3 more winners $\displaystyle (x+3)$, each would get: .$\displaystyle \frac{120}{x+3}$ euro.

This share is 9 euro less than [1]: .$\displaystyle \frac{120}{x+3} \;=\;\frac{120}{x} - 9$

Solve the equation.
. .
I got: $\displaystyle x = 5$