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# If each of three grocery stores receives of a farmer’s

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Joined: 07 Jun 2014
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If each of three grocery stores receives of a farmer’s [#permalink]  26 Apr 2017, 18:15
Expert's post
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Question Stats:

50% (00:50) correct 50% (00:47) wrong based on 16 sessions
If each of three grocery stores receives $$\frac{1}{4}$$ of a farmer’s potato crop, a farmer’s market receives $$\frac{1}{3}$$of the remaining, and a local fast food restaurant receives the remaining 200 pounds, how many pounds of potatoes were in the farmer’s crop?

A. 300
B. 400
C. 900
D. 1,200
E. 1,400

Drill 4
Question: 11
Page: 323
[Reveal] Spoiler: OA

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Sandy
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Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 176

Kudos [?]: 3043 [0], given: 394

Re: If each of three grocery stores receives of a farmer’s [#permalink]  04 May 2017, 01:25
Expert's post
Explanation

Since you know there are 200 lbs remaining after the grocery stores and farmer’s market get their shares, you cannot plug in your own number. So plug in the answers, and start with middle choice (C):

Attachment:

di new1.jpg [ 16.78 KiB | Viewed 2626 times ]

Hence option D is correct!
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Sandy
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Target Test Prep Representative
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Re: If each of three grocery stores receives of a farmer’s [#permalink]  06 Jun 2018, 15:19
Expert's post
sandy wrote:
If each of three grocery stores receives of a farmer’s potato crop, a farmer’s market receives of the remaining, and a local fast food restaurant receives the remaining 200 pounds, how many pounds of potatoes were in the farmer’s crop?

A. 300
B. 400
C. 900
D. 1,200
E. 1,400

e can let n = the total number of pounds of potatoes in the farmer’s crop. Note that 3/4 of his crop went to the grocery stores, leaving 1/4 of the crop remaining. We know that 1/3 of this remaining 1/4 went to the farmer’s market, and the remaining 200 pounds went to the fast food restaurant. We can create the equation:

n = 3(1/4)n + 1/3(1/4)n + 200

n = (3/4)n +(1/12)n + 200

12n = 9n + n + 2400

2n = 2400

n = 1200

Alternate Solution:

We know that 3/4 of the crop went to grocery stores, and (1/3)(1/4) = 1/12 of the crop went to the farmer’s market. Thus, we see that 3/4 + 1/12 = 9/12 + 1/12 = 10/12 of the crop went to these endeavors, leaving 2/12 = 1/6 of the crop, which is equal to 200 pounds, to go to the fast food restaurant. Thus, if we let n = the number of pounds of potatoes in the crop, we see that:

(1/6)n = 200

n = 1200

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# Jeffrey Miller

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Re: If each of three grocery stores receives of a farmer’s [#permalink]  23 Apr 2019, 22:21
sandy wrote:
If each of three grocery stores receives $$\frac{1}{4}$$ of a farmer’s potato crop, a farmer’s market receives $$\frac{1}{3}$$of the remaining, and a local fast food restaurant receives the remaining 200 pounds, how many pounds of potatoes were in the farmer’s crop?

A. 300
B. 400
C. 900
D. 1,200
E. 1,400

Drill 4
Question: 11
Page: 323

i think answer D is correct.

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gogetdeals.co.uk
Re: If each of three grocery stores receives of a farmer’s   [#permalink] 23 Apr 2019, 22:21
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