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A gardener sets 180 plants in row. Each row contains the same number

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Bunuel
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A gardener sets 180 plants in row. Each row contains the same number [#permalink] New post   20 Jul 2019, 03:43
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A gardener sets 180 plants in row. Each row contains the same number of plants. If there were 40 more plants in each row, the gardener would need 6 fewer rows. How many rows are there?

(A) 5
(B) 6
(C) 8
(D) 9
(E) 10
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D
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Re: A gardener sets 180 plants in row. Each row contains the same number [#permalink] New post   20 Jul 2019, 04:05
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Let the number of plants in a row be \(x\) and the number of rows be \(n\)

We have \(xn=180\) or \(x=\frac{180}{n}\)

We are also given that \((x+40)(n-6)=180\)

Substituting for \(x\),

\((\frac{180}{n}+40)(n-6)=180\)

\((180+40n)(n-6)=180n\)

\(180n-1080+40n^2-240n=180n\)

\(40n^2-240n-1080=0\)

\(n^2-6n-27=0\)

\((n-9)(n+3)=0\)

\(n=9\) or \(n=-3\)

Since only non negative values are possible for the number of rows, \(n=9\)

Answer is (D)

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Re: A gardener sets 180 plants in row. Each row contains the same number [#permalink] New post   20 Jul 2019, 04:13
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Bunuel wrote:
A gardener sets 180 plants in row. Each row contains the same number of plants. If there were 40 more plants in each row, the gardener would need 6 fewer rows. How many rows are there?

(A) 5
(B) 6
(C) 8
(D) 9
(E) 10



someone can form equation assigning variable.

I would like to back solve this question.

Option D) 9

Total plants = 180

Total row = 9

Plants in each row: 180 / 9 = 20


If there were 40 more plants in each row:

20 + 40 = 60.

now divide again;

180 / 60 = 3.

now before adding 40 more plants the number of rows was 9 . after adding 40 more trees in each row, we need only 3 row.

Difference of rows = 9 - 3 = 6. which is mentioned in question.
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A gardener sets 180 plants in row. Each row contains the same number [#permalink] New post   20 Jul 2019, 07:38
Can someone please explain what is the gap/flaw in my approach below.


Let number of rows be 'r'.

Therefore total number of plants before and after will be same.(that is after adding 40 plants in each row)

180*r = 220*(r-6)

r = 33


Looking at the solution above.

I guess I interpreted the question wrongly.

A gardener sets 180 plants in row. (I wrongly understood it as 180 plants are planted i one row) I guess this just is the total number of plants that the gardnerer would plan in 'n' (some random number)rows.

Thanks
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Re: A gardener sets 180 plants in row. Each row contains the same number [#permalink] New post   25 Jul 2019, 04:35
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Solution


Given:
    • A gardener sets 180 plants in rows
    • Each row contains the same number of plants
    • If there were 40 more plants in each row, the gardener would need 6 fewer rows

To find:
    • The number of rows

Approach and Working Out:
    • Let the number of rows be x
    • So, total number of plants in a row = \(\frac{180}{x}\)

From the given condition,
    • \(180 = (\frac{180}{x} + 40) * (x – 6)\)
      o Thus, \(\frac{180}{(x - 6)} = \frac{180}{x} - 40\)
      o 180 * 6 = 40 * x * (x – 6)
      o x * (x – 6) = 27 = 8 * 3 = 9 * (9 – 3)

Therefore, x = 9

Hence the correct answer is Option D

Answer: D

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Re: A gardener sets 180 plants in row. Each row contains the same number [#permalink]
25 Jul 2019, 04:35
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