How many people were in the group

Question

A group of people agree to share the cost of a 15000 repair bill to an inn.Before the repairs are made,two more people join the group and enter the agreement.As a result,each person's share is reduced by $250.How many people were in the original group?

Answer 1

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Answer 2

n = number of people originally in group

 

x = cost per person with n member group

 

x = 15000/n  (call this E1)

 

n + 2 = new group number

 

x - 250 = cost per person in (n + 2) member group

 

x - 250 = 15000/(n + 2)  (call this E2)

 

Take x from E1, substitute it into E2, and solve for n:

 

15000/n - 250 = 15000/(n + 2)

 

Divide through by 250:

 

60/n - 1 = 60/(n + 2)

 

Multiply through by n(n + 2) and simplify:

 

60(n + 2) - n(n + 2) = 60n

 

120 - n^2 - 2n = 0

 

n^2 + 2n - 120 = 0 

 

n = (1/2) {-2 ± √[(2)^2 - 4(-120)]} = (1/2)(-2 ± 22)

 

n > 0, so use only the positive square root:

 

n = (1/2)(-2 + 22) = 10

 

You have sufficient information to also get x, and test the solution against the stated premises.