Find $frac1x-y+z$ from given fraction equations.

Clash Royale CLAN TAG#URR8PPP

up vote
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$$beginalign
frac3x,-,frac4y,+,frac2zquad&=quad3\
frac2x,-,frac8y,-,frac1zquad&=,-,8\
frac4x,-,frac6y,-,frac3zquad&=quad1\
frac1x-y+zquad&=quad?
endalign$$
I tried to find solution by equaling $frac1x=a, frac1y=b,$ and $frac1z=c,.$ However, $b=frac14986,$ and $c=frac1443$ which led me to ugly solution or no intended correct solution at all. How to find solution to the above-shown fraction equation?

Thanks beforehand.

systems-of-equations fractions

share|cite|improve this question

edited Jul 23 at 6:40

Parcly Taxel

33.5k136588

asked Jul 23 at 5:33

garakchy

1134

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Seems like an appropriate method; of course, an ugly problem may have an ugly solution...
  – Lord Shark the Unknown
  Jul 23 at 5:36
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Those $b,c$ look right. led me to ugly solution Do you have a reason to expect a pretty solution?
  – dxiv
  Jul 23 at 5:41
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @dxiv The answer choices for this question leads me to think that way. a)2/25 b)30/31 c)31/30 d)19/2 e)25/2
  – garakchy
  Jul 23 at 5:45
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @garakchy There is probably a typo somewhere. Checking with WA 1 / (1/a-1/b+1/c) where 3a-4b+2c=3, 2a-8b-c=-8, 4a-6b-3c=1 gives $5662/15953$ which doesn't match any of those choices.
  – dxiv
  Jul 23 at 5:49
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @dxiv perhaps you are right. Here is image of the question: vgy.me/bvttya.jpg
  – garakchy
  Jul 23 at 6:02
  

  
  
  
  

add a comment | 

up vote
2
down vote

favorite

$$beginalign
frac3x,-,frac4y,+,frac2zquad&=quad3\
frac2x,-,frac8y,-,frac1zquad&=,-,8\
frac4x,-,frac6y,-,frac3zquad&=quad1\
frac1x-y+zquad&=quad?
endalign$$
I tried to find solution by equaling $frac1x=a, frac1y=b,$ and $frac1z=c,.$ However, $b=frac14986,$ and $c=frac1443$ which led me to ugly solution or no intended correct solution at all. How to find solution to the above-shown fraction equation?

Thanks beforehand.

systems-of-equations fractions

share|cite|improve this question

edited Jul 23 at 6:40

Parcly Taxel

33.5k136588

asked Jul 23 at 5:33

garakchy

1134

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Seems like an appropriate method; of course, an ugly problem may have an ugly solution...
  – Lord Shark the Unknown
  Jul 23 at 5:36
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Those $b,c$ look right. led me to ugly solution Do you have a reason to expect a pretty solution?
  – dxiv
  Jul 23 at 5:41
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @dxiv The answer choices for this question leads me to think that way. a)2/25 b)30/31 c)31/30 d)19/2 e)25/2
  – garakchy
  Jul 23 at 5:45
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @garakchy There is probably a typo somewhere. Checking with WA 1 / (1/a-1/b+1/c) where 3a-4b+2c=3, 2a-8b-c=-8, 4a-6b-3c=1 gives $5662/15953$ which doesn't match any of those choices.
  – dxiv
  Jul 23 at 5:49
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @dxiv perhaps you are right. Here is image of the question: vgy.me/bvttya.jpg
  – garakchy
  Jul 23 at 6:02
  

  
  
  
  

add a comment | 

up vote
2
down vote

favorite

up vote
2
down vote

favorite

$$beginalign
frac3x,-,frac4y,+,frac2zquad&=quad3\
frac2x,-,frac8y,-,frac1zquad&=,-,8\
frac4x,-,frac6y,-,frac3zquad&=quad1\
frac1x-y+zquad&=quad?
endalign$$
I tried to find solution by equaling $frac1x=a, frac1y=b,$ and $frac1z=c,.$ However, $b=frac14986,$ and $c=frac1443$ which led me to ugly solution or no intended correct solution at all. How to find solution to the above-shown fraction equation?

Thanks beforehand.

systems-of-equations fractions

share|cite|improve this question

edited Jul 23 at 6:40

Parcly Taxel

33.5k136588

asked Jul 23 at 5:33

garakchy

1134

$$beginalign
frac3x,-,frac4y,+,frac2zquad&=quad3\
frac2x,-,frac8y,-,frac1zquad&=,-,8\
frac4x,-,frac6y,-,frac3zquad&=quad1\
frac1x-y+zquad&=quad?
endalign$$
I tried to find solution by equaling $frac1x=a, frac1y=b,$ and $frac1z=c,.$ However, $b=frac14986,$ and $c=frac1443$ which led me to ugly solution or no intended correct solution at all. How to find solution to the above-shown fraction equation?

Thanks beforehand.

systems-of-equations fractions

share|cite|improve this question

edited Jul 23 at 6:40

Parcly Taxel

33.5k136588

asked Jul 23 at 5:33

garakchy

1134

share|cite|improve this question

share|cite|improve this question

edited Jul 23 at 6:40

Parcly Taxel

33.5k136588

edited Jul 23 at 6:40

Parcly Taxel

33.5k136588

edited Jul 23 at 6:40

Parcly Taxel

33.5k136588

33.5k136588

asked Jul 23 at 5:33

garakchy

1134

asked Jul 23 at 5:33

garakchy

1134

asked Jul 23 at 5:33

garakchy

1134

1134

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Seems like an appropriate method; of course, an ugly problem may have an ugly solution...
  – Lord Shark the Unknown
  Jul 23 at 5:36
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Those $b,c$ look right. led me to ugly solution Do you have a reason to expect a pretty solution?
  – dxiv
  Jul 23 at 5:41
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @dxiv The answer choices for this question leads me to think that way. a)2/25 b)30/31 c)31/30 d)19/2 e)25/2
  – garakchy
  Jul 23 at 5:45
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @garakchy There is probably a typo somewhere. Checking with WA 1 / (1/a-1/b+1/c) where 3a-4b+2c=3, 2a-8b-c=-8, 4a-6b-3c=1 gives $5662/15953$ which doesn't match any of those choices.
  – dxiv
  Jul 23 at 5:49
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @dxiv perhaps you are right. Here is image of the question: vgy.me/bvttya.jpg
  – garakchy
  Jul 23 at 6:02
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  Seems like an appropriate method; of course, an ugly problem may have an ugly solution...
  – Lord Shark the Unknown
  Jul 23 at 5:36
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Those $b,c$ look right. led me to ugly solution Do you have a reason to expect a pretty solution?
  – dxiv
  Jul 23 at 5:41
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @dxiv The answer choices for this question leads me to think that way. a)2/25 b)30/31 c)31/30 d)19/2 e)25/2
  – garakchy
  Jul 23 at 5:45
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @garakchy There is probably a typo somewhere. Checking with WA 1 / (1/a-1/b+1/c) where 3a-4b+2c=3, 2a-8b-c=-8, 4a-6b-3c=1 gives $5662/15953$ which doesn't match any of those choices.
  – dxiv
  Jul 23 at 5:49
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @dxiv perhaps you are right. Here is image of the question: vgy.me/bvttya.jpg
  – garakchy
  Jul 23 at 6:02
  

  
  
  
  

1

1

Seems like an appropriate method; of course, an ugly problem may have an ugly solution...
– Lord Shark the Unknown
Jul 23 at 5:36

Seems like an appropriate method; of course, an ugly problem may have an ugly solution...
– Lord Shark the Unknown
Jul 23 at 5:36

Those $b,c$ look right. led me to ugly solution Do you have a reason to expect a pretty solution?
– dxiv
Jul 23 at 5:41

Those $b,c$ look right. led me to ugly solution Do you have a reason to expect a pretty solution?
– dxiv
Jul 23 at 5:41

@dxiv The answer choices for this question leads me to think that way. a)2/25 b)30/31 c)31/30 d)19/2 e)25/2
– garakchy
Jul 23 at 5:45

@dxiv The answer choices for this question leads me to think that way. a)2/25 b)30/31 c)31/30 d)19/2 e)25/2
– garakchy
Jul 23 at 5:45

@garakchy There is probably a typo somewhere. Checking with WA 1 / (1/a-1/b+1/c) where 3a-4b+2c=3, 2a-8b-c=-8, 4a-6b-3c=1 gives $5662/15953$ which doesn't match any of those choices.
– dxiv
Jul 23 at 5:49

@garakchy There is probably a typo somewhere. Checking with WA 1 / (1/a-1/b+1/c) where 3a-4b+2c=3, 2a-8b-c=-8, 4a-6b-3c=1 gives $5662/15953$ which doesn't match any of those choices.
– dxiv
Jul 23 at 5:49

@dxiv perhaps you are right. Here is image of the question: vgy.me/bvttya.jpg
– garakchy
Jul 23 at 6:02

@dxiv perhaps you are right. Here is image of the question: vgy.me/bvttya.jpg
– garakchy
Jul 23 at 6:02

add a comment | 

1 Answer
1

active

oldest

votes

up vote
3
down vote



accepted

Go on, go on…
$$x=frac43133qquad y=frac86149qquad z=frac4314$$
$$frac1x-y+z=frac566215953=0.3549dots$$
Beauty is not a requirement of mathematical problems – especially in applied problems, and even in pure problems.

share|cite|improve this answer

answered Jul 23 at 5:47

Parcly Taxel

33.5k136588

• 
  
  
  

  
  

  
  
  
  
  
  

  
  thanks. The answer choices to this question looks different from your or my solution. Answer choices are a)2/25 b)30/31 c)31/30 d)19/2 e)25/2. Thanks anyway.
  – garakchy
  Jul 23 at 5:51
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  @garakchy. So, we may suppose one more typo in a textbook !
  – Claude Leibovici
  Jul 23 at 5:54
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @ClaudeLeibovici The open question remains what is the minimal amount of changes/corrections to the posted equations such that one of the book answers works ;-)
  – dxiv
  Jul 23 at 5:59
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @ClaudeLeibovici maybe. Here is image: vgy.me/bvttya.jpg
  – garakchy
  Jul 23 at 6:01
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @dxiv. I tried ... in vain to change the rhs's !
  – Claude Leibovici
  Jul 23 at 6:02
  

  
  
  
  

 | 
show 1 more comment

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
3
down vote



accepted

Go on, go on…
$$x=frac43133qquad y=frac86149qquad z=frac4314$$
$$frac1x-y+z=frac566215953=0.3549dots$$
Beauty is not a requirement of mathematical problems – especially in applied problems, and even in pure problems.

share|cite|improve this answer

answered Jul 23 at 5:47

Parcly Taxel

33.5k136588

• 
  
  
  

  
  

  
  
  
  
  
  

  
  thanks. The answer choices to this question looks different from your or my solution. Answer choices are a)2/25 b)30/31 c)31/30 d)19/2 e)25/2. Thanks anyway.
  – garakchy
  Jul 23 at 5:51
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  @garakchy. So, we may suppose one more typo in a textbook !
  – Claude Leibovici
  Jul 23 at 5:54
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @ClaudeLeibovici The open question remains what is the minimal amount of changes/corrections to the posted equations such that one of the book answers works ;-)
  – dxiv
  Jul 23 at 5:59
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @ClaudeLeibovici maybe. Here is image: vgy.me/bvttya.jpg
  – garakchy
  Jul 23 at 6:01
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @dxiv. I tried ... in vain to change the rhs's !
  – Claude Leibovici
  Jul 23 at 6:02
  

  
  
  
  

 | 
show 1 more comment

up vote
3
down vote



accepted

Go on, go on…
$$x=frac43133qquad y=frac86149qquad z=frac4314$$
$$frac1x-y+z=frac566215953=0.3549dots$$
Beauty is not a requirement of mathematical problems – especially in applied problems, and even in pure problems.

share|cite|improve this answer

answered Jul 23 at 5:47

Parcly Taxel

33.5k136588

• 
  
  
  

  
  

  
  
  
  
  
  

  
  thanks. The answer choices to this question looks different from your or my solution. Answer choices are a)2/25 b)30/31 c)31/30 d)19/2 e)25/2. Thanks anyway.
  – garakchy
  Jul 23 at 5:51
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  @garakchy. So, we may suppose one more typo in a textbook !
  – Claude Leibovici
  Jul 23 at 5:54
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @ClaudeLeibovici The open question remains what is the minimal amount of changes/corrections to the posted equations such that one of the book answers works ;-)
  – dxiv
  Jul 23 at 5:59
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @ClaudeLeibovici maybe. Here is image: vgy.me/bvttya.jpg
  – garakchy
  Jul 23 at 6:01
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @dxiv. I tried ... in vain to change the rhs's !
  – Claude Leibovici
  Jul 23 at 6:02
  

  
  
  
  

 | 
show 1 more comment

up vote
3
down vote



accepted

up vote
3
down vote



accepted

Go on, go on…
$$x=frac43133qquad y=frac86149qquad z=frac4314$$
$$frac1x-y+z=frac566215953=0.3549dots$$
Beauty is not a requirement of mathematical problems – especially in applied problems, and even in pure problems.

share|cite|improve this answer

answered Jul 23 at 5:47

Parcly Taxel

33.5k136588

Go on, go on…
$$x=frac43133qquad y=frac86149qquad z=frac4314$$
$$frac1x-y+z=frac566215953=0.3549dots$$
Beauty is not a requirement of mathematical problems – especially in applied problems, and even in pure problems.

share|cite|improve this answer

answered Jul 23 at 5:47

Parcly Taxel

33.5k136588

share|cite|improve this answer

share|cite|improve this answer

answered Jul 23 at 5:47

Parcly Taxel

33.5k136588

answered Jul 23 at 5:47

Parcly Taxel

33.5k136588

answered Jul 23 at 5:47

Parcly Taxel

33.5k136588

33.5k136588

• 
  
  
  

  
  

  
  
  
  
  
  

  
  thanks. The answer choices to this question looks different from your or my solution. Answer choices are a)2/25 b)30/31 c)31/30 d)19/2 e)25/2. Thanks anyway.
  – garakchy
  Jul 23 at 5:51
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  @garakchy. So, we may suppose one more typo in a textbook !
  – Claude Leibovici
  Jul 23 at 5:54
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @ClaudeLeibovici The open question remains what is the minimal amount of changes/corrections to the posted equations such that one of the book answers works ;-)
  – dxiv
  Jul 23 at 5:59
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @ClaudeLeibovici maybe. Here is image: vgy.me/bvttya.jpg
  – garakchy
  Jul 23 at 6:01
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @dxiv. I tried ... in vain to change the rhs's !
  – Claude Leibovici
  Jul 23 at 6:02
  

  
  
  
  

 | 
show 1 more comment

• 
  
  
  

  
  

  
  
  
  
  
  

  
  thanks. The answer choices to this question looks different from your or my solution. Answer choices are a)2/25 b)30/31 c)31/30 d)19/2 e)25/2. Thanks anyway.
  – garakchy
  Jul 23 at 5:51
  

  
  
  
  


• 
  
  
  

  
  2
  

  
  
  
  
  
  

  
  @garakchy. So, we may suppose one more typo in a textbook !
  – Claude Leibovici
  Jul 23 at 5:54
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @ClaudeLeibovici The open question remains what is the minimal amount of changes/corrections to the posted equations such that one of the book answers works ;-)
  – dxiv
  Jul 23 at 5:59
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  @ClaudeLeibovici maybe. Here is image: vgy.me/bvttya.jpg
  – garakchy
  Jul 23 at 6:01
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  @dxiv. I tried ... in vain to change the rhs's !
  – Claude Leibovici
  Jul 23 at 6:02
  

  
  
  
  

thanks. The answer choices to this question looks different from your or my solution. Answer choices are a)2/25 b)30/31 c)31/30 d)19/2 e)25/2. Thanks anyway.
– garakchy
Jul 23 at 5:51

thanks. The answer choices to this question looks different from your or my solution. Answer choices are a)2/25 b)30/31 c)31/30 d)19/2 e)25/2. Thanks anyway.
– garakchy
Jul 23 at 5:51

2

2

@garakchy. So, we may suppose one more typo in a textbook !
– Claude Leibovici
Jul 23 at 5:54

@garakchy. So, we may suppose one more typo in a textbook !
– Claude Leibovici
Jul 23 at 5:54

@ClaudeLeibovici The open question remains what is the minimal amount of changes/corrections to the posted equations such that one of the book answers works ;-)
– dxiv
Jul 23 at 5:59

@ClaudeLeibovici The open question remains what is the minimal amount of changes/corrections to the posted equations such that one of the book answers works ;-)
– dxiv
Jul 23 at 5:59

@ClaudeLeibovici maybe. Here is image: vgy.me/bvttya.jpg
– garakchy
Jul 23 at 6:01

@ClaudeLeibovici maybe. Here is image: vgy.me/bvttya.jpg
– garakchy
Jul 23 at 6:01

1

1

@dxiv. I tried ... in vain to change the rhs's !
– Claude Leibovici
Jul 23 at 6:02

@dxiv. I tried ... in vain to change the rhs's !
– Claude Leibovici
Jul 23 at 6:02

 | 
show 1 more comment

 

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