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# A certain grocery purchased x pounds of produce for p dollars per poun

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Joined: 02 Sep 2009
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A certain grocery purchased x pounds of produce for p dollars per poun  [#permalink]

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23 Jan 2018, 22:48
00:00

Difficulty:

85% (hard)

Question Stats:

29% (02:24) correct 71% (02:04) wrong based on 36 sessions

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A certain grocery purchased x pounds of produce for p dollars per pound. If y pounds of the produce had to be discarded due to spoilage and the gross profit from the sale of the produce is P. Which of the following represents the price, per pound, of the produce?

A. $$\frac{P + xp}{x - y}$$

B. $$\frac{P + (x - y)p}{x - y}$$

C. $$\frac{P}{x}$$

D. $$\frac{P + xp}{x}$$

E. $$\frac{P - xp}{x - y}$$

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Re: A certain grocery purchased x pounds of produce for p dollars per poun  [#permalink]

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24 Jan 2018, 00:30
1
A

Gross cost price of the produce = x*p

Lets say the selling price per pound of the produce be 's'.

y pounds are discarded. So remaining quantity = x-y

They have to make a profit of 'P' by selling this 'x-y' pounds.

We know Profit=SP-CP.

P = (x-y)*s - x*p

We need 's',

s= (P-x*p)/(x-y). Option A
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Re: A certain grocery purchased x pounds of produce for p dollars per poun  [#permalink]

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26 Jan 2018, 09:38
Bunuel wrote:
A certain grocery purchased x pounds of produce for p dollars per pound. If y pounds of the produce had to be discarded due to spoilage and the gross profit from the sale of the produce is P. Which of the following represents the price, per pound, of the produce?

A. $$\frac{P + xp}{x - y}$$

B. $$\frac{P + (x - y)p}{x - y}$$

C. $$\frac{P}{x}$$

D. $$\frac{P + xp}{x}$$

E. $$\frac{P - xp}{x - y}$$

The cost is xp. We know that profit = revenue - cost.

If we let the selling price per pound = n, then the total revenue is n(x - y); thus, we have:

P = n(x - y) - xp

P + xp = n(x - y)

(P + xp)/(x - y) = n

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Re: A certain grocery purchased x pounds of produce for p dollars per poun &nbs [#permalink] 26 Jan 2018, 09:38
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