SOLUTION: A company has 3000 passengers daily paying a 25 cent fare. For each nickel increase in fare, the company projects it will lose 80 passengers. What fare increase will produce 994 in

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: A company has 3000 passengers daily paying a 25 cent fare. For each nickel increase in fare, the company projects it will lose 80 passengers. What fare increase will produce 994 in      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 98209: A company has 3000 passengers daily paying a 25 cent fare. For each nickel increase in fare, the company projects it will lose 80 passengers. What fare increase will produce 994 in daily revenue?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
let x= a fare increase.
(3000-80x)*(.25+.05x)=994
-4x^2+130x+750=994
subtract 994 from each side. -4x^2+130x-244=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -4x%5E2%2B130x%2B-244+=+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=%28130%29%5E2-4%2A-4%2A-244=12996.

Discriminant d=12996 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-130%2B-sqrt%28+12996+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28130%29%2Bsqrt%28+12996+%29%29%2F2%5C-4+=+2
x%5B2%5D+=+%28-%28130%29-sqrt%28+12996+%29%29%2F2%5C-4+=+30.5

Quadratic expression -4x%5E2%2B130x%2B-244 can be factored:
-4x%5E2%2B130x%2B-244+=+-4%28x-2%29%2A%28x-30.5%29
Again, the answer is: 2, 30.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4%2Ax%5E2%2B130%2Ax%2B-244+%29

30.5 is extraneous because we can't have a 2.5 cent fare increase.
so x=2
2*.05=.10 Ans. fare increase of a dime
Check:
(3000-160)*(.25+.10)=994
2840*.35=994
Ed