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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, 05:29
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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

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Re: PS : NYC Taxi Driver  [#permalink]

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New post 29 Oct 2008, 05:36
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, 05:38
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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: PS : NYC Taxi Driver  [#permalink]

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New post 29 Oct 2008, 05:42
rate*miles*passangers/discount

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

rx3/200

D
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Re: A certain NYC taxi driver  [#permalink]

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New post 24 Jun 2015, 05:24
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
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A certain NYC taxi driver  [#permalink]

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New post 24 Jun 2015, 05:25
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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A certain NYC taxi driver has decided to start charging a  [#permalink]

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New post 26 Sep 2016, 10:22
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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
=

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

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New post 26 Sep 2016, 11:08
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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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Re: A certain NYC taxi driver has decided to start charging a  [#permalink]

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New post 11 Dec 2016, 16:22
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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A certain NYC taxi driver has decided to start charging a  [#permalink]

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New post 03 Jun 2017, 04:25
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: A certain NYC taxi driver has decided to start charging a  [#permalink]

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New post 05 Jun 2017, 08:00
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]

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New post 13 Jul 2018, 09:50
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


Let r=100 cents.
For 3 people, the cost per mile = 3*100 = 300 cents = 3 dollars.
Let x = 2 miles.
Regular cost for 3 people to travel 2 miles = 3*2 = 6 dollars.
With a 50% discount, the cost in dollars = 3. This is our target.

Now we plug x=2 and r=100 into the answers to see which yields our target of 3.
Only D works:
\(\frac{(3xr)}{200} = \frac{(3*2*100)}{200} = 3\)


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

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New post 16 Oct 2018, 10:38
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

Let´s avoid exploring particular cases (undoubtedly very useful) to embrace UNITS CONTROL, one of the most powerful tools of our method!

\(\frac{{r\,\,{\text{cents}}}}{{1\,\,{\text{person}}\,\, \cdot \,\,1\,\,{\text{mile}}}}\,\,\,\,\,\mathop \to \limits^{{\text{discount}}} \,\,\,\,\,\,\,\frac{{\frac{r}{2}\,\,{\text{cents}}}}{{1\,\,{\text{person}}\,\, \cdot \,\,1\,\,{\text{mile}}}}\,\,\,\, = \,\,\,\,\,\frac{1}{2}\,\,\frac{{r\,\,{\text{cents}}}}{{\,\,1\,\,{\text{person}}\,\, \cdot \,\,1\,\,{\text{mile}}}}\)

\(?\,\,\,:\,\,\$ \,\,{\text{for}}\,\,3\,\,{\text{people}}\,\,{\text{for}}\,\,x\,\,{\text{miles}}\,\,\,\left( {{\text{with}}\,\,{\text{discount}}} \right)\)

\(?\,\,\, = \,\,\,3\,\,{\text{person}}\,\,\, \cdot \,\,\,x\,\,{\text{miles}}\,\,\,\left( {\,\frac{1}{2}\,\,\frac{{r\,\,{\text{cents}}}}{{\,\,1\,\,{\text{person}}\,\, \cdot \,\,1\,\,{\text{mile}}}}\,} \right)\,\,\,\left( {\frac{{1\,\,\$ }}{{100\,\,{\text{cents}}}}} \right)\,\,\,\,\, = \,\,\,\,\,\,\$ \,\,\,\frac{{3xr}}{{200}}\,\)

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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