To rent an office, each member of a club must pay n dollars. If two mo

Hi,

info from Q

There are no retrictions on either number of members or amount of payment..
Increase of 2 members results in contribution reducing by 2 dollars..

As member and contribution can be changed, all integers should satisfy the member number..
so E..


BUT lets see by ALGEBRIC way..

let the number of member =x and the contribution be n per member..
so total cost= xn..

in the secon scenario, x increases by 2 and n decreases by 2..
so cost= (x+2)(n-2)..

cost is he same both times, so:-
xn=(x+2)(n-2)..
xn=xn+2n-2x-4..
or 2x=2n-4..
x=n-2...

hence x can take any values, as n changes..
E

If we let m = the number of members in the club, then the total money they will pay for the rental is mn. When two more members join, the number of members is now (m + 2), and now each person pays two dollars less (n - 2). Thus,we can create the equation:

mn = (m + 2)(n - 2)

mn = mn + 2n - 2m - 4

2m = 2n - 4

m = n - 2

We see that the number of members in the club is 2 fewer than the number of dollars contributed per person. Since there is no restriction on the value of n (as long as n is greater than 2), we see that m can be any of the three given values in the Roman numerals.

Answer: E

Let the $Total Cost split evenly among the members = C


I. 16 members

if there are 16 members originally, each member would pay:

N = C / 16

in which case ----> C = 16N

and if 2 more members show up, then the Cost per Member drops by -$2

N - $2 = 16N / 18

18N - 36 = 16N

2N = 36

N = $18

Cost per member could be $18 in the beginning, and there could be 16 members at the beginning

the cost per member would drop to $16 dollars when there are 18 members


I is possible


Testing II -- 17 members

N = C/17

C = 17N

N - $2 = 17N / 19

19N - 38 = 17N

2N = 38

N = 19

the original cost per member could be $19 per member when there is 17 members

the cost per member will drop to $17 per member when there is 19 members


III. 18

n = C/18

C = 18n

n -$2 = 18n / 20

20n - 40 = 18n

2n = 40

n = 20

would cost $20 per member when there was 18 members

then would cost $18 per member when there was 20 members


I, II, and III all work

-E-

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