Problem Solving

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?

I think there are two answers to this question
3xr/2
and
3xr /200

it depends if you take 10 cents or .10 cents. The mgmat gives the second as the correct answer but the first one also works.

The only way that the sec choice could only work if we assume that r cents as eg 10 and if is said r is .dollars then a would work. Am I thinking correct.

Thanks
Khurram



We can solve this as a VIC (Variable In answer Choices) and plug in values for x and r.
r
cents per person per mile
10

x
# of miles
20


Since there are 3 people, the taxi driver will charge them 30 cents per mile.
Since they want to travel 20 miles, the total charge (no discount) would be (30)(20) = 600.
With a 50% discount, the total charge will be 300 cents or 3 dollars.

If we plug r = 10 and x = 20 into the answer choices, the only answer that yields 3 dollars is D.

The correct answer is D.

khurram 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?

I think there are two answers to this question
3xr/2
and
3xr /200

it depends if you take 10 cents or .10 cents. The mgmat gives the second as the correct answer but the first one also works.

You can take 10 cents or .10 dollars - you can't take .10 cents, that changes the entire question. Since the question asks how much does it cost in DOLLARS, that's what we need to convert to for our final answer.

So, the regular rate (in cents) would be:

r * 3 * x

at a 50% discount, it would be:

3rx/2

To convert cents to dollars, we need to divide by 100 (since 100 cents = 1 dollar), so our final answer is:

3rx/2*100 = 3rx/200

Thanks very much, Stuart.

Khurram

Stuart Kovinsky wrote:

khurram 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?

I think there are two answers to this question
3xr/2
and
3xr /200

it depends if you take 10 cents or .10 cents. The mgmat gives the second as the correct answer but the first one also works.

You can take 10 cents or .10 dollars - you can't take .10 cents, that changes the entire question. Since the question asks how much does it cost in DOLLARS, that's what we need to convert to for our final answer.

So, the regular rate (in cents) would be:

r * 3 * x

at a 50% discount, it would be:

3rx/2

To convert cents to dollars, we need to divide by 100 (since 100 cents = 1 dollar), so our final answer is:

3rx/2*100 = 3rx/200

The explantion given as per VIC or whatever method they adapt has pissed me off. THANKS Stuart. They missed the dollar cents part and all is making sense now.

~R

Stuart Kovinsky wrote: So, the regular rate (in cents) would be:

r * 3 * x

at a 50% discount, it would be:

3rx/2

To convert cents to dollars, we need to divide by 100 (since 100 cents = 1 dollar), so our final answer is:

3rx/2*100 = 3rx/200

I set up the equation like so:

(3)(100r)(x)/(200) Where:
3: people
100r: converts rate from cents to dollars
x: miles
200: for the 50% discount in price

Which simplifies down to 3rx/2

What rule or concept am I missing?

Got it. R is in cents (ie 25 cents not 0.25). Had to take a step back.

Doh!