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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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New post 15 Oct 2015, 21:04
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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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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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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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New post 16 Oct 2015, 01:40
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IMO 8000

9 out of 100 corresponds to 720 out of 8000.
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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, 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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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, 19:58
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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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Attached is a visual that should help.
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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 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
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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
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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.



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
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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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New post 03 Feb 2018, 15:36
Hi All,

This question can be solved by TESTing THE ANSWERS. From the prompt, we know that we're going to be doing a number of small calculations AND we're going to end with 720 acres remaining for corn. Since we're asked for the total number of acres, and the answers are all numbers, we just have to work until we find the one that matches what we've been told. In these situations, it's often best to start with Answer B or D. Between those 2 options, D looks 'nicer'/easier, so let's start there.

IF....there were 8000 total acres...

90% was cleared for planting = (.9)(8000) = 7200 acres for planting

Of that land,
40% was soybeans = (4.)(7200) = 2880 acres
50% was wheat = (.5)(7200) = 3600

2880 + 3600 = 6480

7200 - 6480 = 720 --> this is an exact match for what we were told, so this MUST be the answer.

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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 12 May 2018, 03:26
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Quote:
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?


Usually in percentage problems, do not we take final value as 100 and back solve?

Eg: Say total acres of farm owned = 100

Cleared for farming: 90 acres
Of cleared farm: 40% ie 36 acres planted with SB
Of cleared farm: 50% ie 45 acres planted with W
Total SB + W : 91 acres

Remaining 9 acres: planted with corn.

Now 9x= 720 or x = 60

Let us set up a proportion: SB : W: C = 36 : 45 : 9
or 4 :5 : 1 or 10 * x = 600

What is incorrect about this approach ?
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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 12 May 2018, 03:50
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36+45 =81x
now remaining cleared land = 90-81 = 9x
Now 9x = 720: x =80
So total land = 100x = 8000

adkikani wrote:
Quote:
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?


Usually in percentage problems, do not we take final value as 100 and back solve?

Eg: Say total acres of farm owned = 100x

Cleared for farming: 90x acres
Of cleared farm: 40% ie 36 x acres planted with SB
Of cleared farm: 50% ie 45 x acres planted with W
Total SB + W : 91 acres - CALCULATION ERROR

Remaining 9 acres: planted with corn.

Now 9x= 720 or x = 60 again CALCULATION ERROR

Let us set up a proportion: SB : W: C = 36 : 45 : 9
or 4 :5 : 1 or 10 * x = 600
- NOT required. see my approach in last steps

What is incorrect about this approach ?

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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 18 Dec 2018, 05:15
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Another approach is to recognize that 720 = 10% of the cleared land and the cleared land is 90% of the total acreage (A).

Cleared land= 720/0.1= 7,200
Acreage= 7,200/0.9 = 8,000

The answer 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 20 Jun 2019, 23:49
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Quick Soln

given) 10% of 90% =720
So 100%=7200

if 90% of x =7200 ( X is the total acre of land farmer has)
90/100*x =7200
x=7200*100/90
x=8000

Ans choice 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 28 Oct 2019, 10:29
Using the multiplier solution becomes simple
Suppose total land =x
then the equation would be

x*0.90*0.10 (Because 40%+50%=90% and remains 100%-90%=10%)=720

x=8000

Ans. D
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Re: Of the land owned by a farmer, 90 percent was cleared for planting. Of   [#permalink] 28 Oct 2019, 10:29

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

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