Sharing cost. 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 = the number of members currently in the club
200,000/x = 200,000/(x+5) + 2000
Multiply to eliminate fractions.
200,000(x+5) = 200,000x + 2000(x)(x+5)
200,000x + 1,000,000 = 200,000x + 2000x^2 + 10,000x
1,000,000 = 2000x^2 + 10,000x
2000x^2 + 10,000x - 1,000,000 = 0
Divide by 2000.
x^2 + 5x - 500 = 0
(x+25)(x-20) = 0
x = 20, -25
The answer of x=-25 does not make sense in the context, so we are left with x=20 people.
Sharing cost. 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?
To solve this problem, let's assume that there are currently "x" members in the flying club.
Currently, the cost per person is equal to the total cost of the airplane divided by the number of members:
Cost per person = $200,000 / x
If five more people join the club, the total number of members becomes "x + 5".
The new cost per person is equal to the initial cost per person minus the decrease of $2000:
New cost per person = Cost per person - $2000
Now we can set up an equation to solve for the current number of members:
$200,000 / x - $2000 = $200,000 / (x + 5)
To simplify this equation, we can multiply both sides by x to eliminate the denominators:
$200,000 - $2000x = $200,000 - $400,000 / (x + 5)
Multiply both sides of the equation by (x + 5) to eliminate the fraction:
$200,000(x + 5) - $2000x(x + 5) = $400,000
Now distribute and simplify:
$200,000x + $1,000,000 - $2000x^2 - $10,000x = $400,000
Rearrange the equation to form a quadratic equation:
- $2000x^2 - $980,000x + $600,000 = 0
Now we can solve this quadratic equation using various methods such as factoring, completing the square, or using the quadratic formula.
Alternatively, we can use a calculator or algebra software to find the solutions to this equation. The quadratic equation has two solutions: x ≈ -15 and x ≈ 20.
Since the number of members cannot be negative, we discard the solution x ≈ -15. Therefore, the current number of members in the club is approximately 20.
Therefore, there are currently 20 members in the flying club.