Question 205411
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?
;
Let x = no. of members in the club
then
(x+5) = no. of members when 5 more join
:
Do the problem in 1000's of dollars to reduce typing 0's
:
Cost per member now: {{{200/x}}}
Cost per member later: {{{200/((x+5))}}}
:
the equation:
{{{200/x}}} - 2 = {{{200/((x+5))}}}
Multiply by x(x+5)
x(x+5)*{{{200/x}}} - 2x(x+5) = x(x+5)*{{{200/((x+5))}}}
cancel out the denominators
200(x+5) - 2x^2 - 10x = 200x
:
200x + 1000 - 2x^2 - 10x = 200x
Arrange as a quadratic eq on the right
0 = 2x^2 + 10x + 200x - 200x - 1000
:
2x^2 + 10x - 1000 = 0
Simplify, divide by 2
x^2 + 5x - 500 = 0
Factor to:
(x+25)(x-20) = 0
Positive solution:
x = 20 members now.
;
;
Check solution:
200/20 = 10
200/25 = 8
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differ = 2 thousand dollars