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# Becky sets up a hot dog stand in her busy neighborhood and purchases x

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Math Expert
Joined: 02 Sep 2009
Posts: 50615
Becky sets up a hot dog stand in her busy neighborhood and purchases x  [#permalink]

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12 Jan 2015, 09:59
00:00

Difficulty:

25% (medium)

Question Stats:

80% (01:51) correct 20% (02:07) wrong based on 80 sessions

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Becky sets up a hot dog stand in her busy neighborhood and purchases x pounds of hot dogs for p dollars per pound. If she has to throw away s pounds of hot dogs due to spoilage and she sells the rest of the hot dogs for d dollars per pound, which of the following represents the net profit on the sale of the hot dogs?

(A) (x – s)p – sd
(B) xp – (xd – sd)
(C) xd – sp
(D) (x – s)d – xp
(E) (s – p)d – xp

Kudos for a correct solution.

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Re: Becky sets up a hot dog stand in her busy neighborhood and purchases x  [#permalink]

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12 Jan 2015, 10:20
1

The amount of hotdogs she can sell is x-s. The price per pound is d, so the revenue is (x-s)d. The total costs are x time p, so the profit is (x-s)d-xp.
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Re: Becky sets up a hot dog stand in her busy neighborhood and purchases x  [#permalink]

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13 Jan 2015, 00:31
1
aNSWER = (D) (x – s)d – xp

................ Quantity ................... Price .................. Net

Original ......... x .............................. p ..................... xp (Cost Price)

Waste ........... s ............................... p ..................... sp (This is already included in above; not required for calculation)

Good .......... (x-s) ......................... d ............................. (x-s)d

Profit = (x-s)d - xp
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Re: Becky sets up a hot dog stand in her busy neighborhood and purchases x  [#permalink]

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13 Jan 2015, 01:44
1
Here we go -

Expenditure - xp
Revenue - (x-s)d (as s pounds are wasted)

Profit = Revenue - Expenditure -> (x-s)d - xp

Option D.
Math Expert
Joined: 02 Sep 2009
Posts: 50615
Re: Becky sets up a hot dog stand in her busy neighborhood and purchases x  [#permalink]

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19 Jan 2015, 01:18
Bunuel wrote:
Becky sets up a hot dog stand in her busy neighborhood and purchases x pounds of hot dogs for p dollars per pound. If she has to throw away s pounds of hot dogs due to spoilage and she sells the rest of the hot dogs for d dollars per pound, which of the following represents the net profit on the sale of the hot dogs?

(A) (x – s)p – sd
(B) xp – (xd – sd)
(C) xd – sp
(D) (x – s)d – xp
(E) (s – p)d – xp

Kudos for a correct solution.

OFFICIAL SOLUTION:

D. If you want to go to business school, this is a good problem to know how to solve.

profit = gross – costs

To use the formula for profit, you need to know how to figure out Becky’s gross earnings:
Becky’s gross equals the pounds of hot dogs she sold times the selling cost per pound.

The pounds of hot dogs sold is represented by x (the number of pounds she bought) minus s (the number she threw out). The price per pound at which she sold the hot dogs is d. So you can find Becky’s gross earnings using this formula:
Becky’s gross = (x – s)d

Becky’s costs represent how much she paid for all the pounds of hot dogs. The costs equal the amount of hot dogs she bought times the buying cost per pound. So the formula for how much she spent for the hot dogs looks like this:
Becky’s costs = xp

Input the formulas for Becky’s gross and costs into the formula for profit, which gives you this: profit = (x – s)d – xp.

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Re: Becky sets up a hot dog stand in her busy neighborhood and purchases x  [#permalink]

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08 Sep 2018, 04:48
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: Becky sets up a hot dog stand in her busy neighborhood and purchases x &nbs [#permalink] 08 Sep 2018, 04:48
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