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If 6k − 5l = 27 and 3l − 2k = −13 and 5k − 5l = j, what is the value o

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Bunuel
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If 6k − 5l = 27 and 3l − 2k = −13 and 5k − 5l = j, what is the value o [#permalink] New post   22 Jul 2021, 05:00
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If \(6k − 5l = 27\) and \(3l − 2k = −13\) and \(5k − 5l = j\), what is the value of j ?

A. 5
B. 10
C. 15
D. 20
E. 25
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E
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stne
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If 6k − 5l = 27 and 3l − 2k = −13 and 5k − 5l = j, what is the value o [#permalink] New post   03 Aug 2021, 06:57
Bunuel wrote:
If \(6k − 5l = 27\) and \(3l − 2k = −13\) and \(5k − 5l = j\), what is the value of j ?

A. 5
B. 10
C. 15
D. 20
E. 25



We need the value of \(5k − 5l = j\)

or \(5(k − l) = j\)

Hence we need the value of \(k-l\)

\(6k − 5l = 27 (i) \)
\(3l − 2k = −13 (ii)\)

Solving \((i) \) and \((ii)\)
\(l=-3\) and \(k= 2 \)

\(k-l = 5\)

\(j = 5(k-l)\)
\(j= 5*5 = 25\)

Ans-E

Hope it's clear.
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Re: If 6k − 5l = 27 and 3l − 2k = −13 and 5k − 5l = j, what is the value o [#permalink] New post   28 Dec 2021, 06:42
3l−2k=−13 Multiplying the equation by -1, we get: 2k-3l=13

6k−5l=27 ---- (1)
2k-3l=13 ---- (2)
5k−5l=j ---- (3)

Upon adding all the 3 equations, we get: 13k-13l=40+j => k-l=(40+j)/13

From eq (2): k-l = j/5

∴ j/5 = (40+j)/13 => 8j = 200 => j=25 (E)
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Re: If 6k − 5l = 27 and 3l − 2k = −13 and 5k − 5l = j, what is the value o [#permalink] New post   05 Jan 2022, 03:43
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Multiply the second equation with -1; so you get: 2k - 3l = 13
Now add this equation with the first equation to get: 8k - 8l = 40
Now divide both sides through 8 and you get k - l = 5
Since the question was what equals 5k - 5l or 5*(k - l), the answer is E: 25.
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Re: If 6k − 5l = 27 and 3l − 2k = −13 and 5k − 5l = j, what is the value o [#permalink]
05 Jan 2022, 03:43
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