Question 805946: A bus company has 4000 passengers daily, each paying a fare of $2. For each $0.15 increase, the company estimates that it will lose 40 passengers per day.
If the company needs to take in $10450 per day to stay in business, what fare should be charged?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A bus company has 4000 passengers daily, each paying a fare of $2. For each $0.15 increase, the company estimates that it will lose 40 passengers per day.
If the company needs to take in $10450 per day to stay in business, what fare should be charged?
:
let x = no. of .15 increases and no. of 40 passenger losses
:
Write a revenue equation
:
No. of pass * fare amt = $10450
(4000-40x)*(2+.15x) = 10450
FOIL
8000 + 600x - 80x - 6x^2 = 10450
Arrange as a quadratic equation
-6x^2 + 520x + 8000 - 10450 = 0
-6x^2 + 520x - 2450 = 0
Simplify divide by -2
3x^2 - 260x + 1225 = 0
We can use the quadratic equation here, but this will factor to
(3x-245)(x-5) = 0
only one solution is reasonable
x = 5 fare increase of 15 cents
2 + 5(.15) = $2.75 fare to take in $10450
:
This would reduce the passengers to:
4000 - 5(40) = 3800 passengers
:
3800 * 2.75 = 10450, confirms out solution of x=5 ea 15 cent fare increases
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