Question 166061: 10.2 94) sharing cost: The members of a flying club plan to share equally the cost of $200,000 airplane. The members want to find five more people to join the club so that the cost per person will decrease by $2000. How many members are currently in the club?
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! let P = number of people in the club.
let C = Cost for each person
let T = total cost = 200000
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P*C = 200000 (equation 1)
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add 5 people to split the cost and save 2000 per person
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(P+5) * (C-2000) = 200000 (equation 2)
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you have 2 equations to work with:
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multiply out the second equation:
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P*C - 2000*P + 5*C - 10000 = 200000
since P*C equals 200000, then this equation also equals P*C
equation becomes:
P*C - 2000*P + 5*C - 10000 = P*C
subtract P*C from both sides of the equation:
-2000*P + 5*C - 10000 = 0
add 2000*P + 10000 to both sides of the equation:
5*C = 2000*P + 10000
divide both sides of the equation by 5:
C = 400*P + 2000
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in equation 1, substitute 400*P + 2000 for C
that equation becomes:
P * (400*P + 2000) = 200000
multiply out:
400*P^2 + 2000*P = 200000
divide both sides of equation by 400:
P^2 + 5*P = 500
subtract 500 from both sides of equation:
P^2 + 5*P - 500 = 0
solve the quadratic equation:
(P+25) * (P-20) = 0
roots are:
P = -25
or
P = 20
since the number of people can't be negative, P looks like it will be 20.
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if P = 20, then P*C = 200000 becomes 20*C = 200000 which make C = 10000.
likes like original number of people is 20 and original investment each is 10000 dollars.
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P = number of original members = 20.
C = original investment = 10000.
add 5 new members and total members = 25.
divide 200000 by 25 and you get 8000 investment each.
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number of members is 5 more than original (20 + 5 = 25).
amount of investment of each is 2000 less than original investment (10000 - 2000 = 8000).
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