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Find a possible value of a+b given the equations

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Director
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Joined: 17 Dec 2012
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Find a possible value of a+b given the equations  [#permalink]

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New post 03 Jan 2013, 04:36
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Question Stats:

68% (03:06) correct 32% (03:16) wrong based on 126 sessions

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If \(ax + by = 17\) ,
\(2ax + 3by = 43\)

and \(3x =2y\), which of the following is a possible value of \(a+b\) if a and b are integers?

A. 6
B. 10
C. 14
D. 18
E. 20

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Srinivasan Vaidyaraman
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Re: Find a possible value of a+b given the equations  [#permalink]

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New post 03 Jan 2013, 10:30
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SravnaTestPrep wrote:
If \(ax + by = 17\) ,
\(2ax + 3by = 43\)

and \(3x =2y\), which of the following is a possible value of \(a+b\) if a and b are integers?

A. 6
B. 10
C. 14
D. 18
E. 20


Too many variables! I will try to look at the big picture here.
We have two equations:
\(ax + by = 17\) ,
\(2ax + 3by = 43\)

Twice of (ax + by) will be 34 so we get that 'by' must be 43 - 34 = 9
If by = 9, ax must be 17 - 9 = 8

Now, x/y = 2/3
ax/by = (a/b)*(2/3) = 8/9
So a/b = 4/3

Since a and b are integers, many such solutions are possible: a = 4, b = 3 OR a = 8, b = 6 etc. a+b will be 7/14/21...
Answer (C)
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Re: Find a possible value of a+b given the equations  [#permalink]

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New post 11 Sep 2017, 03:59
SravnaTestPrep wrote:
If \(ax + by = 17\) ,
\(2ax + 3by = 43\)

and \(3x =2y\), which of the following is a possible value of \(a+b\) if a and b are integers?

A. 6
B. 10
C. 14
D. 18
E. 20



ax+by=17
2ax+3by=43

multiply first equation by 2 and subtract from 2nd => by=9
multiply 1st equation by 3 and subtract 2nd from it => ax=8

ax=8 and by=9

3x=2y

ax=8
a3x=24
a2y=24
ay=12

ay=12 by=9
a:b= 12/9
starting from least a:b can be => 4:3, 8:6 , 12:9
but second is is that in which we are interested in

a:b = 8:6
a=8 b = 6 a+b =14 OPTION C IS THE ANSWER
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Re: Find a possible value of a+b given the equations   [#permalink] 11 Sep 2017, 03:59
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