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Ninety percent of a large field is cleared for planting. Of the cleare

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Ninety percent of a large field is cleared for planting. Of the cleare  [#permalink]

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New post 20 Mar 2018, 23:13
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Ninety percent of a large field is cleared for planting. Of the cleared land, 50% is planted with blueberry plants and 40% is planted with strawberry plants. If the remaining 360 acres of cleared land is planted with gooseberry plants, what is the size, in acres, of the original field?

(A) 2,916
(B) 3,240
(C) 3,600
(D) 4,000
(E) 8,000

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Re: Ninety percent of a large field is cleared for planting. Of the cleare  [#permalink]

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New post 21 Mar 2018, 00:52
Bunuel wrote:
Ninety percent of a large field is cleared for planting. Of the cleared land, 50% is planted with blueberry plants and 40% is planted with strawberry plants. If the remaining 360 acres of cleared land is planted with gooseberry plants, what is the size, in acres, of the original field?

(A) 2,916
(B) 3,240
(C) 3,600
(D) 4,000
(E) 8,000


IMO D.

10 % of remaining cleared field is 360 acres.
cleared field is 90% of original land.

Hence 10% of 90% of original land = 360 acres
\(0.1 * 0.9 * x = 360\)
\(x = 360 * 100 /9\)
\(x = 4000\) acres

Hence Option D.

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Re: Ninety percent of a large field is cleared for planting. Of the cleare  [#permalink]

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New post 25 Mar 2018, 22:01
Bunuel wrote:
Ninety percent of a large field is cleared for planting. Of the cleared land, 50% is planted with blueberry plants and 40% is planted with strawberry plants. If the remaining 360 acres of cleared land is planted with gooseberry plants, what is the size, in acres, of the original field?

(A) 2,916
(B) 3,240
(C) 3,600
(D) 4,000
(E) 8,000



Given : Let the original land area be X.

0.9*0.1* X = 360
X = 4000

Option D.
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Re: Ninety percent of a large field is cleared for planting. Of the cleare  [#permalink]

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New post 03 Apr 2018, 10:20
Bunuel wrote:
Ninety percent of a large field is cleared for planting. Of the cleared land, 50% is planted with blueberry plants and 40% is planted with strawberry plants. If the remaining 360 acres of cleared land is planted with gooseberry plants, what is the size, in acres, of the original field?

(A) 2,916
(B) 3,240
(C) 3,600
(D) 4,000
(E) 8,000


We can use back-solving here:

Start with the easiest answer choice (D)

Say the original area of field = 4000 acres

90% of 4000 = 3600 acres

Blueberry plants = 50% of 3600 = 1800 acres

Strawberry plants = 40% of 3600 = 1440 acres

BB + SB = 3240 acres

Cleared area - (BB + RB) = 360

3600 - (1800 + 1440) = 360

360 = 360

Hence (D)
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Re: Ninety percent of a large field is cleared for planting. Of the cleare  [#permalink]

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New post 09 Apr 2018, 16:36
Bunuel wrote:
Ninety percent of a large field is cleared for planting. Of the cleared land, 50% is planted with blueberry plants and 40% is planted with strawberry plants. If the remaining 360 acres of cleared land is planted with gooseberry plants, what is the size, in acres, of the original field?

(A) 2,916
(B) 3,240
(C) 3,600
(D) 4,000
(E) 8,000



We can let the area of the original field = n, and thus 0.9n = the area of the cleared field, and create the equation:

(0.5)(0.9n) + (0.4)(0.9n) + 360 = 0.9n

0.45n + 0.36n + 360 = 0.9n

0.81n + 360 = 0.9n

360 = 0.09n

36,000 = 9n

4,000 = n

Alternate Solution:

Let n = the total acreage of the field. We know that 90% of the field is cultivated, and 90% of that cultivation is used for blueberries and strawberries. Thus, 10% of the 90% of the field is cultivated with gooseberries, and this represents 360 acres. Thus, we have:

(0.10)(0.90)n = 360

0.09n = 360

n = 4,000

Answer: D
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Re: Ninety percent of a large field is cleared for planting. Of the cleare   [#permalink] 09 Apr 2018, 16:36
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