How many members were in the club? How much did each one contribute?

Question

The members of a computer club each contributed an equal amount to buy a printer. If there had been three more members, each member would have contributed $10 less. If there had been two fewer members, each member would have contributed $10 more. How many members were in the club? How much did each one contribute?

Answer 1

n = the number of club members

x = the amount each contributed

 

nx = the total cost of the printer

(n+3)(x-10) = nx

nx-10n+3x-30 = nx

-10n+3x = 30              Eq (1)

 

(n-2)(x+10) = nx

nx+10n-2x-20 = nx

 10n -2x = 20               Eq (2)

-10n+3x = 30               Eq (1)   Add

           x = 50

 

10n-2(50) = 20             Eq (2)

10n = 20+100

n = 12

 

12 members

$50 each

Answer 2

Let M = the number of members

Let D = the number of dollars each pays

 

Therefore the Printer , P will cost MD (1)

 

The Printer also will cost (M+3)(D-10)  = MD - 10M + 3D - 30 (2)

 

and it will also cost (M-2)(D+10) = MD + 10M - 2D - 20 (3)

 

set equation 1 = to equation 2

 

set equation 1 = to equation 3

 

MD = MD - 10M + 3D - 30    this results in 30 = -10M + 3D  (4)

MD = MD + 10M - 2D  - 20  this results in 20 = 10M - 2D   (5)

 

Now we solve this system be elimination (Add equations 4 and 5)

 

50 = D      (The price each paid)

 

Plug 50 into any equation 4 or 5

 

I will choose 4,       30 = -10M +150

 

subtract 150

 

-120 = -10 M

 

divide by -10

 

M = 12  (The number of members)