a bus company has 4,000 passengers daily, each paying a fare of $2.00. for each increase of $0.15, the company estimates that it will lose 40 passengers. If the company needs to take in $10,450, per day to stay in business, what fare should be charged.
Need help, in summer school..teacher always busy…any sites that can help would be appreciated.
2006-07-27 11:32:57 · 10 answers · asked by Madina A 2 in Science & Mathematics ➔ Mathematics
(Passengers)(Fare) = Income
Let x = number of 15¢ increases.
Passengers = 4000 - 40x
Fare = 2 + 0.15x
(4000 - 40x)(2 + 0.15x) = 10450 [FOIL]
8000 + 600x - 80x - 6x² = 10450
0 = 6x² - 520x + 2450
By the quadratic formula,
x = { 520 ± √[520² - 4(6)(2450)] } / 2(6)
x = { 520 ± √[270400 - 58800] } / 12
x = { 520 ± √[211600] } / 12
x = { 520 ± 460 } / 12
x = 980 / 12 or x = 60 / 12
x = 245 / 3 or x = 5
Fare = 2 + 0.15x
If x = 5, the fare is 2 + 0.15(5) = 2 + 0.75 = $2.75.
If x = 245 / 3, the fare is 2 + 0.15(245 / 3) = 2 + 12.25 = $14.25.
As many people have pointed out, 5 rate increases to $2.75 would see the bus company have 3800 passengers, for a total of $10450 in income.
If the rate is increased more than that, the company will continue to meet its goal, as long as the fare is below $14.25.
2006-07-27 12:07:26 · answer #1 · answered by Anonymous · 3⤊ 0⤋
So a bus company starts out taking in $8,000 daily (4000 passengers @ $2.00 each).
3960 passengers @ $2.15 each (40 passengers lost each 15 cent increase) = $8,514 for the day
3920 passengers @ $2.30 each = $9,016 for the day
3880 passengers @ $2.45 each = $9,506 for the day
3840 passengers @ $2.60 each = $9,984 for the day
3800 passengers @ $2.75 each = $10,450 for the day
So you'd have to charge $2.75 per passenger per day to stay in business.
2006-07-27 11:39:20 · answer #2 · answered by ensign183 5 · 0⤊ 0⤋
I did the problem exactly like David A with the same results. They will have 3800 passengers @ 2.75 each
2006-07-27 11:47:35 · answer #3 · answered by MollyMAM 6 · 0⤊ 0⤋
Try 4000 x 2 = 8000
$10,450 / 3060 = THINK
2006-07-27 11:39:40 · answer #4 · answered by jinx4swag 3 · 0⤊ 0⤋
4000*2=8000*.15=1200
4000-40=3960*2=7920*.15=1188
10450-1188= 9,262
That means each person need to be charged $2.75
2006-07-27 11:35:00 · answer #5 · answered by Micky L 2 · 0⤊ 0⤋
DO YOUR OWN FLIPPINGGGG HOMEWORK!!!!
i'm not going to cheat for you.
thats not the way you get successful in life.
i may sound like a dork, but i'm better of than you.
*humph.*
2006-07-27 11:36:15 · answer #6 · answered by Anonymous · 0⤊ 0⤋
i think it's 2.75..maybe i'm wrong but that what i think
2006-07-27 11:35:53 · answer #7 · answered by Tara D 2 · 0⤊ 0⤋
2.65
I'll give you an answer, I will NOT show you the math.
TFTP
2006-07-27 11:37:55 · answer #8 · answered by Anonymous · 0⤊ 0⤋
2.75
2006-07-27 11:37:47 · answer #9 · answered by eight beers 3 · 0⤊ 0⤋
it's $2.6125
2006-07-27 11:46:24 · answer #10 · answered by Glam Girl 2 · 0⤊ 0⤋