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?

See:

http://www.jiskha.com/display.cgi?id=1248478864

To solve this problem, let's assume that the current number of members in the flying club is x. We are also trying to find the current number of members in the club.

We know that the cost of the airplane is $200,000, and the cost per person will decrease by $2,000 if five more people join the club. This means the cost per person decreases from (200,000 / x) to (200,000 / (x + 5)), which is a difference of $2,000.

We can set up the following equation to represent the situation:

200,000 / x - 200,000 / (x + 5) = 2,000

To simplify the equation, let's find a common denominator for the fractions, which is x(x + 5):

(200,000 * (x + 5)) - (200,000 * x) = 2,000 * x(x + 5)

Expanding the expression:

200,000x + 1,000,000 - 200,000x = 2,000x^2 + 10,000x

The x terms cancel out:

1,000,000 = 2,000x^2 + 10,000x

Rearranging the equation to set it equal to zero:

2,000x^2 + 10,000x - 1,000,000 = 0

Dividing the equation by 1,000 to simplify it:

2x^2 + 10x - 1,000 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this particular case, factoring is not straightforward, so we will use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 2, b = 10, and c = -1,000. Plugging these values into the quadratic formula:

x = (-10 ± √(10^2 - 4 * 2 * -1,000)) / (2 * 2)

Simplifying:

x = (-10 ± √(100 + 8,000)) / 4
x = (-10 ± √8,100) / 4

Taking the square root:

x = (-10 ± 90) /4

Simplifying further:

x = 80/4 or x = -100/4

Discarding the negative value (-100/4) since the number of club members cannot be negative:

x = 80/4
x = 20

Therefore, there are currently 20 members in the flying club.