Originally Posted by

**Neenoon** Here is the statement: *Many people are sharing a bill. The payment would have been 40cents less per person if they had been 10 people more. In reverse, they would have pay 50 cents more per person if they had been 5 people less. What is the x number of person? And what amount would they each pay?*

Here is what I did:

What I'm looking for:

1. the number of person, x

2. the amount each paid, y

3. the bill amount, xy

What I know:

- the bill would have been 0.40$ less per person if they had been 10 person more. (y-0.40) (x+10) = xy

- the bille would have been 0.50$ more if they had been 5 person less.

(y+0.50) (x-5) = xy

I can simplify both of these:

(y-0.40) (x+10) xy

xy+10y-10x-4=xy

10y-0.40x=4

(y+0.50) (x-5) = xy

xy-5y+0.50x-2.5 = xy

0.50x-5y=2.5 or x-10y=5

Adding those 2 equations:

-0.40x+10y=4

+ x-10y = 5

---------------

0.6x = 9

x = 15

Replacing x and finding y:

(y+0.50) (15-5) = 15y

15y-5y+7.5-2.5 = 15y

-5y = -5

y = 1

So, I get that there are 15 people and they each paid 1$

Is there something wrong in this?