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For a particular model of moving truck, rental agency A charges a dail [#permalink]

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22 Oct 2014, 04:48

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For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

(A) \(\frac{100(m-p)}{q-n}\)

(B) \(\frac{200(p-m)}{n-q}\)

(C) \(\frac{50(m-p)}{q-n}\)

(D) \(\frac{2(p-m)}{n-q}\)

(E) \(\frac{m-p}{2(q-n)}\)

Let x be the number of miles this driver must drive for the two rental agencies’ total charges to be equal.

Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile). Agency B's charges for two days = 2p + q/100*x (q/100 gives dollars per mile).

Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

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22 Oct 2014, 10:41

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This is mostly like a plug and chug. Let the # of days =2 and the # of miles be equal for both drivers. Just remember to divide n and q by 100 to convert from cents to dollars.

Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

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24 Oct 2014, 00:08

Bunuel wrote:

chetan86 wrote:

For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

(A) \(\frac{100(m-p)}{q-n}\)

(B) \(\frac{200(p-m)}{n-q}\)

(C) \(\frac{50(m-p)}{q-n}\)

(D) \(\frac{2(p-m)}{n-q}\)

(E) \(\frac{m-p}{2(q-n)}\)

Let x be the number of miles this driver must drive for the two rental agencies’ total charges to be equal.

Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile). Agency B's charges for two days = 2p + q/100*x (q/100 gives dollars per mile).

Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

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24 Oct 2014, 13:40

Bunuel wrote:

chetan86 wrote:

For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

(A) \(\frac{100(m-p)}{q-n}\)

(B) \(\frac{200(p-m)}{n-q}\)

(C) \(\frac{50(m-p)}{q-n}\)

(D) \(\frac{2(p-m)}{n-q}\)

(E) \(\frac{m-p}{2(q-n)}\)

Let x be the number of miles this driver must drive for the two rental agencies’ total charges to be equal.

Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile). Agency B's charges for two days = 2p + q/100*x (q/100 gives dollars per mile).

For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

(A) \(\frac{100(m-p)}{q-n}\)

(B) \(\frac{200(p-m)}{n-q}\)

(C) \(\frac{50(m-p)}{q-n}\)

(D) \(\frac{2(p-m)}{n-q}\)

(E) \(\frac{m-p}{2(q-n)}\)

Let x be the number of miles this driver must drive for the two rental agencies’ total charges to be equal.

Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile). Agency B's charges for two days = 2p + q/100*x (q/100 gives dollars per mile).

Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

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09 Jan 2016, 14:19

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

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18 Jul 2016, 02:00

Bunuel wrote:

chetan86 wrote:

For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

(A) \(\frac{100(m-p)}{q-n}\)

(B) \(\frac{200(p-m)}{n-q}\)

(C) \(\frac{50(m-p)}{q-n}\)

(D) \(\frac{2(p-m)}{n-q}\)

(E) \(\frac{m-p}{2(q-n)}\)

Let x be the number of miles this driver must drive for the two rental agencies’ total charges to be equal.

Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile). Agency B's charges for two days = 2p + q/100*x (q/100 gives dollars per mile).

Hi Bunuel, Could you please explain why you are taking the number of miles for both the agencies as equal. Couldn't it be possible that - Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile). Agency B's charges for two days = 2p + q/100*y (q/100 gives dollars per mile).

For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

(A) \(\frac{100(m-p)}{q-n}\)

(B) \(\frac{200(p-m)}{n-q}\)

(C) \(\frac{50(m-p)}{q-n}\)

(D) \(\frac{2(p-m)}{n-q}\)

(E) \(\frac{m-p}{2(q-n)}\)

Let x be the number of miles this driver must drive for the two rental agencies’ total charges to be equal.

Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile). Agency B's charges for two days = 2p + q/100*x (q/100 gives dollars per mile).

Hi Bunuel, Could you please explain why you are taking the number of miles for both the agencies as equal. Couldn't it be possible that - Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile). Agency B's charges for two days = 2p + q/100*y (q/100 gives dollars per mile).

And the total miles would be x+y.

Thanks

The question asks: which of the following expressions gives the number of miles (x in our case) this driver must drive for the two rental agencies’ total charges to be equal? So, for what x, are the charges of two agencies equal.
_________________

For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

(A) \(\frac{100(m-p)}{q-n}\)

(B) \(\frac{200(p-m)}{n-q}\)

(C) \(\frac{50(m-p)}{q-n}\)

(D) \(\frac{2(p-m)}{n-q}\)

(E) \(\frac{m-p}{2(q-n)}\)

Let x be the number of miles this driver must drive for the two rental agencies’ total charges to be equal.

Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile). Agency B's charges for two days = 2p + q/100*x (q/100 gives dollars per mile).

Hi Bunuel, Could you please explain why you are taking the number of miles for both the agencies as equal. Couldn't it be possible that - Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile). Agency B's charges for two days = 2p + q/100*y (q/100 gives dollars per mile).

Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

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18 Jul 2016, 03:46

Hi Bunuel, Could you please explain why you are taking the number of miles for both the agencies as equal. Couldn't it be possible that - Agency A's charges for two days = 2m + n/100*x (n/100 gives dollars per mile). Agency B's charges for two days = 2p + q/100*y (q/100 gives dollars per mile).

Got it. Thank you. I was thinking about another possibility in which the driver could travel x miles for agency A and y miles for agency B and still get the total charges as equal.

Re: For a particular model of moving truck, rental agency A charges a dail [#permalink]

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15 Sep 2017, 03:51

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

For a particular model of moving truck, rental agency A charges a daily fee of m dollars, plus n cents per mile. For the same model of truck, rental agency B charges a daily fee of p dollars, plus q cents per mile. If a driver plans to rent this model of truck for two days, which of the following expressions gives the number of miles this driver must drive for the two rental agencies’ total charges to be equal?

(A) \(\frac{100(m-p)}{q-n}\)

(B) \(\frac{200(p-m)}{n-q}\)

(C) \(\frac{50(m-p)}{q-n}\)

(D) \(\frac{2(p-m)}{n-q}\)

(E) \(\frac{m-p}{2(q-n)}\)

We can create the following equation in which z = the number of miles driven. Since the daily fee is in dollars and the mileage fee is in cents, we convert the daily fee to cents. We should remember that m dollars = 100m cents and p dollars = 100p cents.

2(100m) + nz = 2(100p) + qz

200m + nz = 200p + qz

nz - qz = 200p - 200m

z(n - q) = 200(p - m)

z = 200(p - m)/(n - q)

Answer: B
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