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

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

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29 Oct 2008, 05:29
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Difficulty:

65% (hard)

Question Stats:

57% (01:23) correct 43% (01:20) wrong based on 780 sessions

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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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29 Oct 2008, 05:36
D

Almost stepped into the trap

3xr/2 is in cents - 3xr/200 dollars
Director
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Posts: 671
Re: PS : NYC Taxi Driver  [#permalink]

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29 Oct 2008, 05:38
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1
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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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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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

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A certain NYC taxi driver  [#permalink]

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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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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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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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11 Dec 2016, 16:22
zahraf wrote:
I think the correct answer is A
if it is D please inform me why/

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

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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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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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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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Re: A certain NYC taxi driver has decided to start charging a   [#permalink] 16 Oct 2018, 10:38
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