SOLUTION: A group plans to start a new business that will require $240,000 for start-up capital. The individuals in the group share the cost eually. If two addiditonal people join the group,

Question 426651: A group plans to start a new business that will require $240,000 for start-up capital. The individuals in the group share the cost eually. If two addiditonal people join the group, the cost per person will decrease by $4000. How many people are presently in the group?
I let:
Capital: C = 240,000
People: P
Cost per person: I = 4000 - 2P
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!



Hi

Let P represent the number in the original group

 240000/P - 240000/(P+2)= $4000

 240000[(P+2) - P] = 4000*P(P+2)

   4000P^2 + 8000P - 480000 = 0

       P^2 + 2P - 120 = 0

factoring

     (P+12)(P-10) = 0

     (P+12)= 0  tossing out the negative solution for count

     (P-10)= 0   P = 10, original group.  (Would be 12 if 2 more joined)

CHECKING our Answer***

  240,000/10 = 24,000

  240,000/12 = 20,000

     24,000-20,000 = $4000 

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