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

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Difficulty:   95% (hard)

Question Stats: 40% (02:22) correct 60% (02:31) wrong based on 597 sessions

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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?

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

Originally posted by chetan86 on 22 Oct 2014, 04:48.
Last edited by Bunuel on 22 Oct 2014, 07:15, edited 1 time in total.
Edited the question.
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Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

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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).

Equate and solve for x:

$$2m + \frac{n}{100}*x=2p + \frac{q}{100}*x$$;

$$200m+nx=200p+qx$$;

$$x=\frac{200p-200m}{n-q}$$.

Hope it's clear.

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

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1
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.

You should get 2m+n*miles/100 = 2p + q*miles/100

Solving for miles gets you B.
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Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

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1
Bunuel , chetan2u

Can you please explain why we need to divide the cents in 100?
I understand that n/100 gives dollars per mile, but why can't we leave it as cents? (i.e., why do we need to say p cents is 0.0n when its already mentioned that n is cents?)

Hi..

When we are finding the cost one way it is some dollars as a constant and some cents per mile..
So, if you have to add both, we have to get them into same units, either dollars or cents...

Say you take 1 hour for first few miles and then takes 30 minutes to complete the rest ..
Total cannot be 1+30, it will be 1+ (30/60) as we have to convert both into same units
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Manager  Joined: 17 Oct 2012
Posts: 60
Location: India
Concentration: Strategy, Finance
WE: Information Technology (Computer Software)
Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

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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).

Equate and solve for x:

$$2m + \frac{n}{100}*x=2p + \frac{q}{100}*x$$;

$$200m+nx=200p+qx$$;

$$x=\frac{200p-200m}{n-q}$$.

Hope it's clear.

Hi Bunuel,
Thanks a lot for your explanation.
Next time I will take care to formulate mathematical expression correctly. Thanks for the link.
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Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

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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).

Equate and solve for x:

$$2m + \frac{n}{100}*x=2p + \frac{q}{100}*x$$;

$$200m+nx=200p+qx$$;

$$x=\frac{200p-200m}{n-q}$$.

Hope it's clear.

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

Hi Bunuel,
Can you please clarify why we are not multiplying 2 days to cents? I was stuck on this question because I calculated as 2(m + n/100)
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Posts: 58958
Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

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pairakesh10 wrote:
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).

Equate and solve for x:

$$2m + \frac{n}{100}*x=2p + \frac{q}{100}*x$$;

$$200m+nx=200p+qx$$;

$$x=\frac{200p-200m}{n-q}$$.

Hope it's clear.

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

Hi Bunuel,
Can you please clarify why we are not multiplying 2 days to cents? I was stuck on this question because I calculated as 2(m + n/100)

Because x is already the total number of miles driven in two days.
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Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

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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).

Equate and solve for x:

$$2m + \frac{n}{100}*x=2p + \frac{q}{100}*x$$;

$$200m+nx=200p+qx$$;

$$x=\frac{200p-200m}{n-q}$$.

Hope it's clear.

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
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Posts: 58958
Re: For a particular model of moving truck, rental agency A charges a dail  [#permalink]

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gmat730 wrote:
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).

Equate and solve for x:

$$2m + \frac{n}{100}*x=2p + \frac{q}{100}*x$$;

$$200m+nx=200p+qx$$;

$$x=\frac{200p-200m}{n-q}$$.

Hope it's clear.

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

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gmat730 wrote:
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).

Equate and solve for x:

$$2m + \frac{n}{100}*x=2p + \frac{q}{100}*x$$;

$$200m+nx=200p+qx$$;

$$x=\frac{200p-200m}{n-q}$$.

Hope it's clear.

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

To understand better check similar questions:
salesperson-a-s-compensation-for-any-week-is-360-plus-30977.html
health-insurance-plan-a-requires-the-insured-to-pay-1000-or-106447.html

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

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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[/quote]

To understand better check similar questions:
salesperson-a-s-compensation-for-any-week-is-360-plus-30977.html
health-insurance-plan-a-requires-the-insured-to-pay-1000-or-106447.html

Hope it helps.[/quote]

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

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

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)

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

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Bunuel , chetan2u

Can you please explain why we need to divide the cents in 100?
I understand that n/100 gives dollars per mile, but why can't we leave it as cents? (i.e., why do we need to say p cents is 0.0n when its already mentioned that n is cents?)

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

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chetan2u wrote:
Bunuel , chetan2u

Can you please explain why we need to divide the cents in 100?
I understand that n/100 gives dollars per mile, but why can't we leave it as cents? (i.e., why do we need to say p cents is 0.0n when its already mentioned that n is cents?)

Hi..

When we are finding the cost one way it is some dollars as a constant and some cents per mile..
So, if you have to add both, we have to get them into same units, either dollars or cents...

Say you take 1 hour for first few miles and then takes 30 minutes to complete the rest ..
Total cannot be 1+30, it will be 1+ (30/60) as we have to convert both into same units

Oh boy...
you're right, totally missed that.

Thank you very much chetan2u ! Re: For a particular model of moving truck, rental agency A charges a dail   [#permalink] 24 Nov 2018, 05:17
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