SOLUTION: a group of friends bought a gift for $60 when 3 more people chipped in, each share decreased by $1.00. How many people contributed in the end and much did they pay?

Question 629485: a group of friends bought a gift for $60 when 3 more people chipped in, each share decreased by $1.00. How many people contributed in the end and much did they pay?
Answer by rajagopalan(174) (Show Source): You can put this solution on YOUR website!
scene 1..
Let the Number of friends=x
Let the initial contribution =y
we get 1 equation x*y=60
we can write y=60/x
..
scene 2..
number of fiends=x+3
fresh contribution =y-1
we get equation2 (x+3)*(y-1)=60
expand eqn 2 & equate it to 1
xy=xy+3y-3-x
0=3y-x-3...eqn3
substitute y=60/x in eqn 3
0=3(60/x)-x-3
{(180-x^2-3x)/x}=0
x^2+3x-180=0
x^2+15x-12x-180=0
x(x+15)-12(x+15)=0
(x+15)(x-12)=0
x=-15 or 12
ignore negative value
we get number of initial friends=12
additional friends=3
Total friends=12+3=15
each contributed 60/15=4 dollars
cheers

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