SOLUTION: 94. 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

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: 94. 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      Log On


   

Question 170960: 94. 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?
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
200000/x=c where x is the number of people in the club
:
200000/x+5=c-2000
:
so 200000%2F%28x%2B5%29=%28200000%2Fx%29-2000---> multiply all terms by x(x+5)
:
200000x=200000%28x%2B5%29-2000%28x%5E2%2B5x%29distribute
:
200000x=200000x%2B1000000-2000x%5E2-10000x 200000x terms cancel each other and divide rest of terms by 2000.
:
-x%5E2-5x%2B500=0--->x^2+5x-500=0}}}
20 and -25 are the values for x but we know there arent negative people so 20 is our value for x meaning that
:
THERE ARE CURRENTLY20 PEOPLE IN THE CLUB
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B5x%2B-500+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%285%29%5E2-4%2A1%2A-500=2025.

Discriminant d=2025 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+2025+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+2025+%29%29%2F2%5C1+=+20
x%5B2%5D+=+%28-%285%29-sqrt%28+2025+%29%29%2F2%5C1+=+-25

Quadratic expression 1x%5E2%2B5x%2B-500 can be factored:
1x%5E2%2B5x%2B-500+=+1%28x-20%29%2A%28x--25%29
Again, the answer is: 20, -25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-500+%29