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Of the land owned by a farmer, 90 percent was cleared for planting. Of

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Of the land owned by a farmer, 90 percent was cleared for planting. Of [#permalink]

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Of the land owned by a farmer, 90 percent was cleared for planting. Of the cleared land, 40 percent was planted with soybeans and 50 percent of the cleared land was planted with wheat. If the remaining 720 acres of cleared land was planted with corn, how many acres did the farmer own?

(A) 5,832
(B) 6,480
(C) 7,200
(D) 8,000
(E) 8,889


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[Reveal] Spoiler: OA

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Re: Of the land owned by a farmer, 90 percent was cleared for planting. Of [#permalink]

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New post 15 Oct 2015, 22:14
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Bunuel wrote:
Of the land owned by a farmer, 90 percent was cleared for planting. Of the cleared land, 40 percent was planted with soybeans and 50 percent of the cleared land was planted with wheat. If the remaining 720 acres of cleared land was planted with corn, how many acres did the farmer own?

(A) 5,832
(B) 6,480
(C) 7,200
(D) 8,000
(E) 8,889


Kudos for a correct solution.


40% od 90% = 36%, 50% 0f 90% = 45% so the remaining 90-45-36=9%=720 acres or 10% of 90%=9% --> 720/9*100=80o0 acres Answer (D)
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Re: Of the land owned by a farmer, 90 percent was cleared for planting. Of [#permalink]

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New post 16 Oct 2015, 01:14
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Percentage cleared for planting = 90
Soybean = 40% of 90 = 36 % of total
Wheat = 50 % of 90 =45 % of total
Corn = 10 % of 90 = 9 % of total

Since 9% of total = 720 acres
Therefore , total land = 720/9 * 100 = 8000 acres
:)
Answer D
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Re: Of the land owned by a farmer, 90 percent was cleared for planting. Of [#permalink]

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IMO 8000

9 out of 100 corresponds to 720 out of 8000.

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New post 16 Oct 2015, 17:52
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Let farmer has X land;
Cleaned =.9 x
out of .9 x 10% is 720 ; therefore .09x=720 => x=8000

Hence answer is D

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Of the land owned by a farmer, 90 percent was cleared for planting. Of the cleared land, 40 percent was planted with soybeans and 50 percent of the cleared land was planted with wheat. If the remaining 720 acres of cleared land was planted with corn, how many acres did the farmer own?

(A) 5,832
(B) 6,480
(C) 7,200
(D) 8,000
(E) 8,889

For this type of Question its always better to go by option and elimination plays a key role here .

As per the Q -- out of the total land -- 90% was cleared for planting .

now see the option --- only B,C, D will give you a integer value .When we do 90% of total Area.

hence A,E can be eliminated .

Option B -- 6480 * (90/100) = 5832
5832 * ( 40/100 ) = wont give us a integer value . Hence can be eliminated .

Option C and D left .
Now see option D is good number to start with because its value .( 8000)

When we apply 8000( 90/100) = 7200 (50/100) = 3600
7200(40/100)= 2880

Now sum them = 2880 + 3600 = 6480

If the remaining 720 acres of cleared land was planted with corn .

This remaining area comes from 7200 - 6480 = 720 .

Hence the condition got satisfied .

Ans is D .
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Re: Of the land owned by a farmer, 90 percent was cleared for planting. Of [#permalink]

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New post 02 May 2016, 07:55
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Bunuel wrote:
Of the land owned by a farmer, 90 percent was cleared for planting. Of the cleared land, 40 percent was planted with soybeans and 50 percent of the cleared land was planted with wheat. If the remaining 720 acres of cleared land was planted with corn, how many acres did the farmer own?

(A) 5,832
(B) 6,480
(C) 7,200
(D) 8,000
(E) 8,889


Kudos for a correct solution.


Solution:

We can start by letting T = the total land owned by the farmer. Since 90% was cleared for farming we can say:

0.9T = cleared for farming

We are next given that of the cleared land, 40 percent was planted with soybeans. This can be represented as:

0.4(0.9T) = planted with soybeans

0.36T = planted with soybeans

Next we are given that 50 percent of the cleared land was planted with wheat. This can be represented as:

0.5(0.9T) = 0.45T

Finally, we are given that the remaining 720 acres of cleared land was planted with corn. Thus, we can create the following equation:

0.36T + 0.45T + 720 = 0.9T

0.81T + 720 = 0.9T

720 = 0.09T

72,000 = 9T

T = 8,000

Answer: D
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Re: Of the land owned by a farmer, 90 percent was cleared for planting. Of [#permalink]

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Attached is a visual that should help.
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Screen Shot 2016-05-10 at 5.48.46 PM.png
Screen Shot 2016-05-10 at 5.48.46 PM.png [ 67.68 KiB | Viewed 5988 times ]


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New post 10 May 2016, 18:58
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(10% of (90% of total land)) is 720

\(0.1 * 0.9 * X = 720\)

\(X = 8000\)

Option D
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Re: Of the land owned by a farmer, 90 percent was cleared for planting. Of [#permalink]

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New post 21 Jun 2016, 10:12
I understand it the following way:
0.40(90)+0.50(90)+720=0.90x
2880+3600+720=0.90x
7200=0.90x
\(\frac{7200}{0.90}\)=x
8000=x

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Of the land owned by a farmer, 90 percent was cleared for planting. Of [#permalink]

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New post 24 Jun 2016, 03:55
Bunuel wrote:
Of the land owned by a farmer, 90 percent was cleared for planting. Of the cleared land, 40 percent was planted with soybeans and 50 percent of the cleared land was planted with wheat. If the remaining 720 acres of cleared land was planted with corn, how many acres did the farmer own?

(A) 5,832
(B) 6,480
(C) 7,200
(D) 8,000
(E) 8,889


Kudos for a correct solution.



Suppose the total land was 100. Then, 90% of 100 = 90.

Of the 90, 40%(36) of land was used for soyabeans, 50%(45) was for wheat. Remaining land portion of 90 is 9.

According to question 9 equals 720.

By unitary method.
If;
9(land) = 720
then;
100(land) =x(what).

By cross multiplication.

x = \(720*100/9\)

= 8000.

D.

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Re: Of the land owned by a farmer, 90 percent was cleared for planting. Of [#permalink]

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New post 13 Nov 2016, 22:23
Hi,

Is this a right approach [or an unnecessarily longer one?]

In the cleared land : 720 is 10%
Hence, 720*4 = 2880 is 40%
and, 720*5 = 3600 is 50%

Adding all these the 90% cleared land turns out to be 7200, the remaining has to be 800. Hence 7200+800 = 8000 -> Answer D.

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Re: Of the land owned by a farmer, 90 percent was cleared for planting. Of [#permalink]

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New post 22 Dec 2016, 13:37
0.4 x 0.9X = 0.36X = Soybean
0.5 x 0.9X = 0.45X = Wheat
0.36x + 0.45x + 720 = 0.9x
0.81x + 720 = 0.9x
x = 8000
D
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Re: Of the land owned by a farmer, 90 percent was cleared for planting. Of [#permalink]

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Re: Of the land owned by a farmer, 90 percent was cleared for planting. Of   [#permalink] 31 Dec 2017, 01:38
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