SOLUTION: The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to find five more people to join the club so that the cost per person will decr

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Question 150245This question is from textbook Elementary and Intermediate Algebra
: The members of a flying club plan to share equally the cost of a $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? This question is from textbook Elementary and Intermediate Algebra

Answer by mangopeeler07(462) About Me  (Show Source):
You can put this solution on YOUR website!
constant=cost in thousands *(so you have less zeros and it looks less confusing)
y=number of people
x=price per person

200/y=x
(200/y+5)=x-2

Substitute x
(200/y+5)=(200/y)-2

Common denominator on the right side=y
200/y+5=200/y - 2y/y

Combine like terms on the right side
200/y+5=200-2y/y

Cross multiply
200y=(y+5)(-2y+200)

FOIL the right side
200y=-2y^2+190y+1000

Subtract 200y from both sides
0=-2y^2-10y+1000

Factor out a negative 2
0=-2(y^2+5y-500)

Factor
0=-2(y+25)(y-20)

Solve for y
y+25=0
y=-25

y-20=0
y=20

You got two solutions, but since y=number of people, and the amount of people cannot be negative, you know that y=20 is your answer.

# of current members: 20