SOLUTION: A restaurant bill that comes to �200 is to be divided equally among a group of people. However, three people leave before the bill is settled and the remainder of the group has to

Question 575297: A restaurant bill that comes to �200 is to be divided equally among a group of people. However, three people leave before the bill is settled and the remainder of the group has to pay an extra �15 each.
How many people were orginally in the group?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A restaurant bill that comes to �200 is to be divided equally among a group of people.
However, three people leave before the bill is settled and the remainder of the group has to pay an extra �15 each.
How many people were originally in the group?
:
let x = no. originally in the group
then
= amt each should have paid
and
= amt that was paid
:
- = 15
multiply by x(x-3)
x(x-3)* - x(x-3)* = 15x(x-3)
Cancel the denominators and you have
200x - 200(x-3) = 15x^2 - 45x
200x - 200x + 600 = 15x^2 - 45x
Combine on the right to form a quadratic equation
0 = 15x^2 - 45x - 600
Simplify, divide by 15
x^2 - 3x - 40 = 0
factors to
(x-8)(x+5) = 0
positive solution
x = 8 people in the original group
;
:
see if this checks, find out how much should be paid and was paid
200/8 = 25
200/5 = 40
------------
differs by $15
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