SOLUTION: Hi the members of a club each contribute an equal amount to buy a computer. If there were 3 more members each member would have contributed 10 dollars less. If there were 2 fewer

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Question 1137213: Hi
the members of a club each contribute an equal amount to buy a computer. If there were 3 more members each member would have contributed 10 dollars less. If there were 2 fewer members each would have contributed 10 dollars more.
how many members were in the club.
thanks
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Let the number of members be x, and the amount they each contribute be y. Then

%28x%2B3%29%28y-10%29+=+xy
xy-10x%2B3y-30+=+xy
-10x%2B3y+=+30 (1)

and

%28x-2%29%28y%2B10%29+=+xy
xy%2B10x-2y-20+=+xy
10x-2y+=+20 (2)

Adding (1) and (2) eliminates x and gives us the value of y:
y+=+50

Then substituting y=50 in either (1) or (2) gives us x=12.

ANSWER: The number of members in the club is x = 12.

CHECK:
xy = 12(50) = 600
(x+3)(y-10) = 15(40) = 600
(x-2)(x+10) = 10(60) = 600

Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let n be the number of members and " r " be how much every member contributes in the base version.


Then from the condition you have these 2 equations

nr = (n+3)*(r-10),    (1)
nr = (n-2)*(r+10).    (2)


Simplify (1) and (2) step by step:


nr = nr + 3r - 10n - 30,   (3)   ( instead of (1) )
nr = nr - 2r + 10n - 20.   (4)   ( instead of (2) )


0 =  3r - 10n - 30,        (5)   ( instead of (3) )
0 = -2r + 10n - 20,        (6)   ( instead of (4) )


Add equations (5) and (6). You will get


0 = r -30 - 20,   or

r = 50.


Then from (6)  10n = 2r + 20 = 2*50 + 20 = 120.  Hence,  n= 120/10 = 12.


Answer.  The number of members is 12.  Each contributes 50 dollars.


CHECK.   You may check the answer on your own by substituting the found values into equations (1) and (2).

         Do it - it is VERY educational in this sort of problems.

Solved.

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