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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
(A) 5
(B) 6
(C) 8
(D) 9
(E) 10
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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)
Posted from my mobile device
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)
Posted from my mobile device
20 Jul 2019, 04:13
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Bunuel
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
(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.
