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If each of three grocery stores receives 1/4 of a farmer’s potato crop

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If each of three grocery stores receives 1/4 of a farmer’s potato crop  [#permalink]

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New post 05 Jun 2018, 03:09
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If each of three grocery stores receives 1/4 of a farmer’s potato crop, a farmer’s market receives 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

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Re: If each of three grocery stores receives 1/4 of a farmer’s potato crop  [#permalink]

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New post 05 Jun 2018, 04:57
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Bunuel 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



Bunuel.... please review ( and explain :-) ) the question .... if possible.
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Re: If each of three grocery stores receives 1/4 of a farmer’s potato crop  [#permalink]

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New post 05 Jun 2018, 05:01
u1983 wrote:
Bunuel 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



Bunuel.... please review ( and explain :-) ) the question .... if possible.

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Edited the stem. Thank you.
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Re: If each of three grocery stores receives 1/4 of a farmer’s potato crop  [#permalink]

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New post 05 Jun 2018, 05:13
Bunuel wrote:
u1983 wrote:
Bunuel 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



Bunuel.... please review ( and explain :-) ) the question .... if possible.

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Edited the stem. Thank you.



Thanks a bunch Bunnuel for the help.


Each of three grocery stores receives 1/4 of a farmer’s potato crop. They receives in total = \(3* \frac{1}{4}\)=\(\frac{3}{4}\)
Hence remaining = \(1 - \frac{3}{4}\)=\(\frac{1}{4}\)

According to the Q-stem : a farmer’s market receives 1/3 of the remaining, and a local fast food restaurant receives the remaining 200 pounds
Thus 200 pounds = 2/3 of the remaining after the 3 grocers=\(\frac{2}{3} * \frac{1}{4}\)= \(\frac{1}{6}\)

Hence The total portal of the farmed potato= 6*200=1200 pounds
Hence I would go with option D.
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Re: If each of three grocery stores receives 1/4 of a farmer’s potato crop  [#permalink]

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New post 05 Jun 2018, 06:03
1

Solution



Given:
    • Each grocery store receives \(\frac{1}{4}\) of a farmer’s potato crop
    • A farmer’s market receives \(\frac{1}{3}\) of the remaining
    • A local fast food restaurant receives the remaining 200 pounds

To find:
    • Total amount of potatoes (in pounds) in the farmer’s crop

Approach and Working:
If we assume the total amount of potatoes to be x pounds, then
    • Grocery stores received = \(3 * \frac{x}{4} = \frac{3x}{4}\)
    • Farmer’s market received = \(\frac{1}{3} (x – \frac{3x}{4}) = \frac{1}{3} * \frac{x}{4} = \frac{x}{12}\)
    • Remaining crop = \(x – (\frac{3x}{4} + \frac{x}{12}) = x – \frac{5x}{6} = \frac{x}{6}\)

Given that, \(\frac{x}{6}\) = 200
    Or, x = 200 * 6 = 1200 pounds

Hence, the correct answer is option D.

Answer: D
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Re: If each of three grocery stores receives 1/4 of a farmer’s potato crop  [#permalink]

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New post 05 Jun 2018, 18:36
Bunuel wrote:
If each of three grocery stores receives 1/4 of a farmer’s potato crop, a farmer’s market receives 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

(1) Each of 3 grocery stores gets \(\frac{1}{4}\) of the potato crop
\(3*\frac{1}{4}=\frac{3}{4}\) is gone,
and \(\frac{1}{4}\) remains

(2) \(\frac{1}{3}\) of the remaining \(\frac{1}{4}\) goes to a farmer's market

\((\frac{1}{3}*\frac{1}{4})=\frac{1}{12}\) more is gone

FRACTION GONE:\((\frac{3}{4}+\frac{1}{12})=\frac{10}{12}\) gone, and

FRACTION LEFT
\((1-\frac{10}{12})=(\frac{12}{12}-\frac{10}{12})=\frac{2}{12}=\frac{1}{6}\) remains

(3) How many pounds of potatoes, P, were there to begin with?

200 lbs of potatoes remain
\(\frac{1}{6}\) of \(P\) remains
\(200=\frac{1}{6}P\)
\(P=1,200\)

Answer D
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Re: If each of three grocery stores receives 1/4 of a farmer’s potato crop  [#permalink]

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New post 06 Jun 2018, 16:35
Bunuel wrote:
If each of three grocery stores receives 1/4 of a farmer’s potato crop, a farmer’s market receives 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


We 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
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Re: If each of three grocery stores receives 1/4 of a farmer’s potato crop  [#permalink]

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New post 30 Oct 2018, 04:02
Bunuel wrote:
If each of three grocery stores receives 1/4 of a farmer's potato crop, a farmer's market receives 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



let the total be x

1. each of the three grocery stores receives 1/4 = 3x/4
2. a farmer's market receives 1/3 of the remaining = (x/4)*1/3 = x/12
remaining = x - (3x/4 + x/12) = 200
x -(10x/12) = x/6 = 200
x=1200


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Re: If each of three grocery stores receives 1/4 of a farmer’s potato crop  [#permalink]

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New post 30 Oct 2018, 08:48
If each of three grocery stores receives 1/4 of a farmer's potato crop, a farmer's market receives 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?
Sol-
farmer's potato crop be x
three grocery stores -x/4 each
farmer's market = 1/3 (x-(3x/4)) = x/12
rest =200

total= 200+(x/12)+3x/4 = x
=> x= 1200 (D)
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Re: If each of three grocery stores receives 1/4 of a farmer’s potato crop   [#permalink] 30 Oct 2018, 08:48
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