SOLUTION: A group plans to share the cost equally for a $200,000 plane,the group wants to find 5 more people to join ,so that the cost will decrease $2,000 per person .How people are curren

Click here to see ALL problems on Quadratic Equations

Question 282341: A group plans to share the cost equally for a $200,000 plane,the group wants to find 5 more people to join ,so that the cost will decrease $2,000 per person .How people are currently in the group.

Found 5 solutions by mananth, Theo, ikleyn, n2, josgarithmetic:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website!
let the people in the group be x
cost / person = 200000/x
increase by 5
x+5
200000/x+5
200000 /x -2000 = 200000/x+5
200000 -2000x /x = 200000 / x+5
200000x -10000x +1000000 = 200000x
-10000x=-1000000
Number of people now
x=100

Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
cost of the plane is $200,000

There are x number of people in the group.

If the group adds 5 people, there will be x+5 people in the group and the cost per person will be $2,000

The cost per person would be the total cost divided by the number of people in the group.

Your equation would be:

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

Multiply both sides of this equaqtion by (x+5) to get:

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

Divide both sides of this equation by $2,000 to get:

100 = x + 5

Subtract 5 from each side of this equation to get:

x = 95

There are 95 people originally in this group.

They add 5 and the number of people in the group becomes 100.

$200,000 / 100 = $2,000 per person.

Answer by ikleyn(53742)   (Show Source):
You can put this solution on YOUR website!
.
A group plans to share the cost equally for a $200,000 plane, the group wants to find 5 more people to join,
so that the cost will decrease $2,000 per person. How people are currently in the group ?
~~~~~~~~~~~~~~~~~~~~~~

        The solution by @mananth is incorrect due to arithmetic errors inside of it.
        I came to bring a correct solution.

The original scenario is dollars per person. The other scenario is dollars per person. The setup equation is - = 2000. Divide both side by 1000 to make writing easier - = 2. Reduce it to the quadratic equation x^2 + 5x - 5000 = 0. Factor left side (x+25)*(x-20) = 0. The roots are x= -25 and x= 20. Since we look for a price, we accept the positive root and reject the negative one. ANSWER. Currently/originally the group is 20 people.

Solved correctly.

Answer by n2(78)   (Show Source):
You can put this solution on YOUR website!
.
A group plans to share the cost equally for a $200,000 plane, the group wants to find 5 more people to join,
so that the cost will decrease $2,000 per person. How people are currently in the group ?
~~~~~~~~~~~~~~~~~~~~~~~

The original scenario is dollars per person. The other scenario is dollars per person. The setup equation is - = 2000. Divide both side by 1000 to make writing easier - = 2. Reduce it to the quadratic equation x^2 + 5x - 5000 = 0. Factor left side (x+25)*(x-20) = 0. The roots are x= -25 and x= 20. Since we look for a price, we accept the positive root and reject the negative one. ANSWER. Currently/originally the group consists of 20 people.

Solved.

Answer by josgarithmetic(39790)   (Show Source):
You can put this solution on YOUR website!

PRICE PEOPLE COST 200000/n n 200000 200000/(n+5) n+5 200000 DIFF. 2000