A certain NYC taxi driver has decided to start charging a

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
=

rate*miles*passangers/discount

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

rx3/200

D

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

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



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) \(\frac{3xr}{200}\)

Hi zahraf

You seem to have missed converting Cents in to Dollars

I hope it helps!

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

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!

3xr/2 in cents
3xr/200 in dollar

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:
\(\frac{(3xr)}{200} = \frac{(3*2*100)}{200} = 3\)

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.

A great candidate for plugging in values.

Let r = 50 and x = 10.

This means, the NYC taxi driver charges 50 cents per person per mile.

Therefore, cost of travelling 10 miles for ONE person = 50 * 10 = 500 cents
Hence, cost of travelling 10 miles for THREE people = 500 * 3 = 1500 cents.

However, he does give them a 50% discount, therefore,
Effective cost of travelling 10 miles for THREE people = \(\frac{1500 }{ 2}\) = 750 cents.

Here’s when we have to be extremely careful about the conversion, the answer is expected in terms of dollars and not cents, therefore,
Effective cost of travelling 10 miles for THREE people = \(\frac{750 }{ 100}\) = 7.5 dollars, since 100 cents equals 1 dollar.

Substituting the value of x and r in the options, the expression shown in answer option D gives 7.5

Note that the expression shown in answer option A gives 750. This is a trap, because the cost is 750 cents and not 750 dollars.

The correct answer option is D.

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