Question 207398

Let the current amount of members be M


Since the cost of the plane is $200,000, then the current cost, per 

person is: {{{200000/M}}}


Since they wish to get 5 more members, then the new amount of members then would be:

M + 5


Therefore, the new cost, then, per person would be: {{{200000/(M + 5)}}}


Now, since the cost per person would decrease by $2,000 when 5 new members are admitted, then we get: {{{200000/M - 200000/(M + 5) = 2000}}}


200,000(M + 5) - 200,000(M) = 2,000(M)(M + 5) ------> Multiplying entire equation by LCD, M(M + 5)


{{{200000M + 1000000 - 200000M = 2000M^2 + 10000M}}}  

{{{2000M^2 + 10000M - 1000000 = 0}}} 

{{{2000(M^2 + 5M - 500) = 0}}}

{{{M^2 + 5M - 500 = 0}}}


(M + 25)(M - 20) = 0


M = - 25, or 20

Ignore M = - 25, so M = 20


Therefore, the current amount of members in the club is {{{highlight_green(20)}}}, but will change to 25 (20 + 5) after 5 new ones are admitted.

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Check
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Current amount of members: 20. Cost per person = {{{200000/20}}} = $10,000.


New amount of members after 5 new ones are admitted: 25 (20 + 5). New cost per person then would be: {{{200000/25}}} = $8,000.


Reduction in price per person then would be $2,000 ($10,000 - $8,000)