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If each of three grocery stores receives of a farmer’s
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26 Apr 2017, 18:15
26 Apr 2017, 18:15
Expert Reply
00:00
Question Stats:
58% (01:20) correct
41% (01:07) wrong based on 24 sessions
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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
A. 300
B. 400
C. 900
D. 1,200
E. 1,400
Drill 4
Question: 11
Page: 323
Question: 11
Page: 323
Re: If each of three grocery stores receives of a farmer’s
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04 May 2017, 01:25
04 May 2017, 01:25
Expert Reply
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):
di new1.jpg [ 16.78 KiB | Viewed 5959 times ]
Hence option D is correct!
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 5959 times ]
Hence option D is correct!
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Re: If each of three grocery stores receives of a farmer’s
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06 Jun 2018, 15:19
06 Jun 2018, 15:19
Expert Reply
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
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
Answer: D
