Problem Solving

A group of 10 people plan to contribute equally to pay fora friend's gift that costs G dollars. If nadditional people want to contribute to pay for the gift, the required contribution per person will be reduced by how many dollars?
(A)Gn/100+10n
(B)10+n/Gn
(C)10G+Gn/n
(D)Gn+10G/GN-10
(E)10G/n^2+10n :roll:
answer after discussion...[/img]

Just substitute easy numbers.

Let the gift cost $100, so initially everyone pays $10 each.

Let n = 10 (10 additional people contribute), the cost per head now will be 100/20 = $5.

Sub G = 100 and n = 10 in the answer choices, you should get 5 as answer. Only A satisfies IMO.

Infact you could even use smaller numbers.

IMO A
Cost of the gift = G
Total people initially = 10
Cost per head = G/10

Extra people who want to contribute = n
So, total # of people = 10+n
Cost per head now= G/(10+n)

Notice that G/10 > G/(10+n) [now each person has to contribute less]

So, contribution per person will be reduced = [G/10]- [G/(10+n)] = Gn/10(10+n)=Gn/100+10n

Clearly A

thanks a lot..