Can anyone help me for this first degree floor function equation?












-3












$begingroup$


Find $y$ such that



$$lfloor y rfloor + lfloor 3y rfloor = 5$$



First, I use the properties that $$n leq y <n+1$$
And suppose



$$lfloor yrfloor = 5-n$$



and



$$lfloor 3yrfloor = n$$



But I’m stuck, could anyone help me?






functions







share|cite|improve this question











$endgroup$












  • $begingroup$
    Do you just need one example of such a $y$ (in which case you could just try some reasonable guesses until you find one), or do you want a description of all the solutions $y$ (which is also easy, but better done by thinking than by trial and error).
    $endgroup$
    – Andreas Blass
    Nov 14 '18 at 15:00






  • 5




    $begingroup$
    @HavanaTime Please do not vandalize the post after you have received an answer. Doing so can get you into trouble on this site.
    $endgroup$
    – Brahadeesh
    Dec 15 '18 at 4:40
















-3












$begingroup$


Find $y$ such that



$$lfloor y rfloor + lfloor 3y rfloor = 5$$



First, I use the properties that $$n leq y <n+1$$
And suppose



$$lfloor yrfloor = 5-n$$



and



$$lfloor 3yrfloor = n$$



But I’m stuck, could anyone help me?






functions







share|cite|improve this question











$endgroup$












  • $begingroup$
    Do you just need one example of such a $y$ (in which case you could just try some reasonable guesses until you find one), or do you want a description of all the solutions $y$ (which is also easy, but better done by thinking than by trial and error).
    $endgroup$
    – Andreas Blass
    Nov 14 '18 at 15:00






  • 5




    $begingroup$
    @HavanaTime Please do not vandalize the post after you have received an answer. Doing so can get you into trouble on this site.
    $endgroup$
    – Brahadeesh
    Dec 15 '18 at 4:40














-3












-3








-3


1



$begingroup$


Find $y$ such that



$$lfloor y rfloor + lfloor 3y rfloor = 5$$



First, I use the properties that $$n leq y <n+1$$
And suppose



$$lfloor yrfloor = 5-n$$



and



$$lfloor 3yrfloor = n$$



But I’m stuck, could anyone help me?






functions







share|cite|improve this question











$endgroup$




Find $y$ such that



$$lfloor y rfloor + lfloor 3y rfloor = 5$$



First, I use the properties that $$n leq y <n+1$$
And suppose



$$lfloor yrfloor = 5-n$$



and



$$lfloor 3yrfloor = n$$



But I’m stuck, could anyone help me?






functions




functions






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 15 '18 at 13:02









Brahadeesh

6,36442363




6,36442363










asked Nov 14 '18 at 14:48









Havana TimeHavana Time

12




12












  • $begingroup$
    Do you just need one example of such a $y$ (in which case you could just try some reasonable guesses until you find one), or do you want a description of all the solutions $y$ (which is also easy, but better done by thinking than by trial and error).
    $endgroup$
    – Andreas Blass
    Nov 14 '18 at 15:00






  • 5




    $begingroup$
    @HavanaTime Please do not vandalize the post after you have received an answer. Doing so can get you into trouble on this site.
    $endgroup$
    – Brahadeesh
    Dec 15 '18 at 4:40


















  • $begingroup$
    Do you just need one example of such a $y$ (in which case you could just try some reasonable guesses until you find one), or do you want a description of all the solutions $y$ (which is also easy, but better done by thinking than by trial and error).
    $endgroup$
    – Andreas Blass
    Nov 14 '18 at 15:00






  • 5




    $begingroup$
    @HavanaTime Please do not vandalize the post after you have received an answer. Doing so can get you into trouble on this site.
    $endgroup$
    – Brahadeesh
    Dec 15 '18 at 4:40
















$begingroup$
Do you just need one example of such a $y$ (in which case you could just try some reasonable guesses until you find one), or do you want a description of all the solutions $y$ (which is also easy, but better done by thinking than by trial and error).
$endgroup$
– Andreas Blass
Nov 14 '18 at 15:00




$begingroup$
Do you just need one example of such a $y$ (in which case you could just try some reasonable guesses until you find one), or do you want a description of all the solutions $y$ (which is also easy, but better done by thinking than by trial and error).
$endgroup$
– Andreas Blass
Nov 14 '18 at 15:00




5




5




$begingroup$
@HavanaTime Please do not vandalize the post after you have received an answer. Doing so can get you into trouble on this site.
$endgroup$
– Brahadeesh
Dec 15 '18 at 4:40




$begingroup$
@HavanaTime Please do not vandalize the post after you have received an answer. Doing so can get you into trouble on this site.
$endgroup$
– Brahadeesh
Dec 15 '18 at 4:40










2 Answers
2






active

oldest

votes


















1












$begingroup$

Hint: write y as $n+d$ .Now the first term turns out to be n and for second term take cases for $0<d<1/3$ ,$1/3<=d<2/3$ and $2/3<=d<1$. Can you do after that ?






share|cite|improve this answer









$endgroup$













  • $begingroup$
    answer should be $(4/3,5/3)$
    $endgroup$
    – Atharva Kathale
    Nov 14 '18 at 15:38



















1












$begingroup$

Hint: $1$ is too small and $2$ is too big. So any values of $y$ will have to be between $1$ and $2$.



For $y$ between $1$ and $2$, $lfloor y rfloor = 1$.



So you just have to pick values that get the $lfloor 3y rfloor$ term to come out right.






share|cite|improve this answer









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    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    1












    $begingroup$

    Hint: write y as $n+d$ .Now the first term turns out to be n and for second term take cases for $0<d<1/3$ ,$1/3<=d<2/3$ and $2/3<=d<1$. Can you do after that ?






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      answer should be $(4/3,5/3)$
      $endgroup$
      – Atharva Kathale
      Nov 14 '18 at 15:38
















    1












    $begingroup$

    Hint: write y as $n+d$ .Now the first term turns out to be n and for second term take cases for $0<d<1/3$ ,$1/3<=d<2/3$ and $2/3<=d<1$. Can you do after that ?






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      answer should be $(4/3,5/3)$
      $endgroup$
      – Atharva Kathale
      Nov 14 '18 at 15:38














    1












    1








    1





    $begingroup$

    Hint: write y as $n+d$ .Now the first term turns out to be n and for second term take cases for $0<d<1/3$ ,$1/3<=d<2/3$ and $2/3<=d<1$. Can you do after that ?






    share|cite|improve this answer









    $endgroup$



    Hint: write y as $n+d$ .Now the first term turns out to be n and for second term take cases for $0<d<1/3$ ,$1/3<=d<2/3$ and $2/3<=d<1$. Can you do after that ?







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered Nov 14 '18 at 15:08









    Atharva KathaleAtharva Kathale

    889




    889












    • $begingroup$
      answer should be $(4/3,5/3)$
      $endgroup$
      – Atharva Kathale
      Nov 14 '18 at 15:38


















    • $begingroup$
      answer should be $(4/3,5/3)$
      $endgroup$
      – Atharva Kathale
      Nov 14 '18 at 15:38
















    $begingroup$
    answer should be $(4/3,5/3)$
    $endgroup$
    – Atharva Kathale
    Nov 14 '18 at 15:38




    $begingroup$
    answer should be $(4/3,5/3)$
    $endgroup$
    – Atharva Kathale
    Nov 14 '18 at 15:38











    1












    $begingroup$

    Hint: $1$ is too small and $2$ is too big. So any values of $y$ will have to be between $1$ and $2$.



    For $y$ between $1$ and $2$, $lfloor y rfloor = 1$.



    So you just have to pick values that get the $lfloor 3y rfloor$ term to come out right.






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      Hint: $1$ is too small and $2$ is too big. So any values of $y$ will have to be between $1$ and $2$.



      For $y$ between $1$ and $2$, $lfloor y rfloor = 1$.



      So you just have to pick values that get the $lfloor 3y rfloor$ term to come out right.






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        Hint: $1$ is too small and $2$ is too big. So any values of $y$ will have to be between $1$ and $2$.



        For $y$ between $1$ and $2$, $lfloor y rfloor = 1$.



        So you just have to pick values that get the $lfloor 3y rfloor$ term to come out right.






        share|cite|improve this answer









        $endgroup$



        Hint: $1$ is too small and $2$ is too big. So any values of $y$ will have to be between $1$ and $2$.



        For $y$ between $1$ and $2$, $lfloor y rfloor = 1$.



        So you just have to pick values that get the $lfloor 3y rfloor$ term to come out right.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 14 '18 at 15:04









        paw88789paw88789

        29.2k12349




        29.2k12349






























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