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

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Math Expert
Joined: 02 Sep 2009
Posts: 58454
If each of three grocery stores receives 1/4 of a farmer’s potato crop  [#permalink]

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05 Jun 2018, 03:09
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35% (medium)

Question Stats:

79% (01:41) correct 21% (02:04) wrong based on 39 sessions

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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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05 Jun 2018, 04:57
1
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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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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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.

______________________
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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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.

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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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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
$$200=\frac{1}{6}P$$
$$P=1,200$$

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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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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

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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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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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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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