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A certain NYC taxi driver has decided to start charging a

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A certain NYC taxi driver has decided to start charging a [#permalink]

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New post 29 Oct 2008, 06:29
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A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?

A. 3xr/2
B. 3x/200r
C. 3r/200x
D. 3xr/200
E. xr/600
[Reveal] Spoiler: OA

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A certain NYC taxi driver has decided to start charging a [#permalink]

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amitdgr wrote:
A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?

A. 3xr/2
B. 3x/200r
C. 3r/200x
D. 3xr/200
E. xr/600


Here's an algebraic approach:

A certain taxi driver charges a rate of r CENTS per person per mile
r CENTS = r/100 DOLLARS [e.g., 3 cents = 3/100 dollars]
Since there are 3 people, the rate is (3)(r/100) DOLLARS per mile
In other words, the rate is 3r/100 dollars per mile.
With a 50% discount, the new rate = (1/2)(3r/100)
In other words, the discounted rate = 3r/200 dollars per mile.

[how much] would it cost three people to travel x miles?
TOTAL cost = (rate)(distance)
= (3r/200 dollars per mile)(x miles)
= 3rx/200 dollars
=
[Reveal] Spoiler:
D


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Re: PS : NYC Taxi Driver [#permalink]

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New post 29 Oct 2008, 06:38
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r/100 dollars per person per mile

one person going x miles will be charged rx/100
50% discount = rx/200

3such people = 3rx/200

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Re: A certain NYC taxi driver has decided to start charging a [#permalink]

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amitdgr wrote:
A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?

A. 3xr/2
B. 3x/200r
C. 3r/200x
D. 3xr/200
E. xr/600


Quote:
The taxi driver is charging : At a rate of r cents per person per mile.


So, Charges for 3 people to travel x miles will be : \(3*x*r\)% => \(\frac{3rx}{100}\)

Quote:
he decides to give them a 50% discount


Charges for 3 people to travel x miles will be : \(\frac{3rx}{100} * 50\)% => \(\frac{3rx}{100}*\frac{50}{100}\) = \(\frac{3xr}{200}\)

So, Answer will be (D) \(\frac{3xr}{200}\)
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A certain NYC taxi driver has decided to start charging a [#permalink]

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Test values:
let r be 100, so r equals 100 cents or $1. Now the driver charges for one person $1 per mile, that means he will charge for 3 people $3 per mile.
Now let x equals 2. For 2 miles the driver will charge now for the 3 people $6. Now consider the 50% discount, which leads to the final charge of $3 for the 3 people.
If you plug in now the values x=2, r=100 you will get for A 300, which is the amount in cents but the question clearly states that we want the amount in dollars.
Only option D yields 3 and thus is a match.
D is the answer!

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Re: PS : NYC Taxi Driver [#permalink]

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New post 29 Oct 2008, 06:36
D

Almost stepped into the trap :)

3xr/2 is in cents - 3xr/200 dollars

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Re: PS : NYC Taxi Driver [#permalink]

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New post 29 Oct 2008, 06:42
rate*miles*passangers/discount

discount has to be in dollars so 1/2/100/1=200

rx3/200

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Re: A certain NYC taxi driver [#permalink]

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zahraf wrote:
A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in
dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?
A. 3xr / 2
B.3x / 200r
C. 3r / 200x
D.3xr / 200
E. xr / 600



Charge for One person and One mile = r cents
i.e. Charge for 3 persons and One mile = 3*r cents
i.e. Charge for 3 persons and 'x' miles = 3*r*x cents

After Discount, Charge = 50% of (3*r*x) cents
i.e. Charged Amount = (1/2)*(3*r*x) cents

But 1 Dollar = 100 Cents

i.e. Charged Amount in Dollar = (1/2)*(3*r*x)/100 Dollars
i.e. Charged Amount in Dollar = (3*r*x)/200 Dollars

Answer: Option
[Reveal] Spoiler:
D

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A certain NYC taxi driver [#permalink]

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New post 24 Jun 2015, 06:25
zahraf wrote:
I think the correct answer is A
if it is D please inform me why/


Hi zahraf

You seem to have missed converting Cents in to Dollars

I hope it helps! :)
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Re: A certain NYC taxi driver has decided to start charging a [#permalink]

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New post 11 Dec 2016, 17:22
zahraf wrote:
I think the correct answer is A
if it is D please inform me why/

Answer asked for how many dollars not cents
100 cent equal to 1 dollar. Need to convert it to Dollar means divided by 100

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Re: A certain NYC taxi driver has decided to start charging a [#permalink]

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New post 05 Jun 2017, 09:00
3xr/2 in cents
3xr/200 in dollar

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Re: A certain NYC taxi driver has decided to start charging a   [#permalink] 05 Jun 2017, 09:00
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