Need help explaining method of calculation for a school question for my $10$ year old

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A family friend sent us an example question that said a child starting secondary / high school would have in their first year. We tried showing it to my 10 year old who was unable to do it, after having a look myself I don't know either. The question is as follows:



Abe, Ben and Ceri's total score playing a video game was $4665$.
Ben scored $311$ fewer than Abe but $3$ times more than Ceri.
How many points did Ceri score?



I've seen what claims to be the answer, but I couldn't explain how it was right. Can anyone explain, please?




problem-solving




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    A family friend sent us an example question that said a child starting secondary / high school would have in their first year. We tried showing it to my 10 year old who was unable to do it, after having a look myself I don't know either. The question is as follows:



    Abe, Ben and Ceri's total score playing a video game was $4665$.
    Ben scored $311$ fewer than Abe but $3$ times more than Ceri.
    How many points did Ceri score?



    I've seen what claims to be the answer, but I couldn't explain how it was right. Can anyone explain, please?




    problem-solving




    share|cite|improve this question
























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      A family friend sent us an example question that said a child starting secondary / high school would have in their first year. We tried showing it to my 10 year old who was unable to do it, after having a look myself I don't know either. The question is as follows:



      Abe, Ben and Ceri's total score playing a video game was $4665$.
      Ben scored $311$ fewer than Abe but $3$ times more than Ceri.
      How many points did Ceri score?



      I've seen what claims to be the answer, but I couldn't explain how it was right. Can anyone explain, please?




      problem-solving




      share|cite|improve this question














      A family friend sent us an example question that said a child starting secondary / high school would have in their first year. We tried showing it to my 10 year old who was unable to do it, after having a look myself I don't know either. The question is as follows:



      Abe, Ben and Ceri's total score playing a video game was $4665$.
      Ben scored $311$ fewer than Abe but $3$ times more than Ceri.
      How many points did Ceri score?



      I've seen what claims to be the answer, but I couldn't explain how it was right. Can anyone explain, please?





      problem-solving





      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Aug 26 at 20:28







      user550230

















      asked Aug 26 at 19:54









      GrandMasterFlush

      1034




      1034




















          2 Answers
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          3
          down vote



          accepted










          Let's remove $311$ points from Abe, without affecting Ben and Ceri. So now the total is $4665 - 311 = 4354$, and Abe and Ben each have $3$ times as much as Ceri.
          Together, Abe, Ben and Ceri have $3+3+1=7$ times as much as Ceri. So Ceri has
          $4354/7 = 622$ points.






          share|cite|improve this answer




















          • Thank you, I've been able to explain it to my daughter now (after learning myself!).
            – GrandMasterFlush
            Aug 26 at 20:12

















          up vote
          2
          down vote













          Let the scores be $A,B,C$ with the obvious notation. Then we have $$A+B+C=4665quad&quad B=A-311quad &quad B=3Cimplies$$ $$implies A+(A-311)+frac A-3113=4665$$



          Can you finish from here?






          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








            up vote
            3
            down vote



            accepted










            Let's remove $311$ points from Abe, without affecting Ben and Ceri. So now the total is $4665 - 311 = 4354$, and Abe and Ben each have $3$ times as much as Ceri.
            Together, Abe, Ben and Ceri have $3+3+1=7$ times as much as Ceri. So Ceri has
            $4354/7 = 622$ points.






            share|cite|improve this answer




















            • Thank you, I've been able to explain it to my daughter now (after learning myself!).
              – GrandMasterFlush
              Aug 26 at 20:12














            up vote
            3
            down vote



            accepted










            Let's remove $311$ points from Abe, without affecting Ben and Ceri. So now the total is $4665 - 311 = 4354$, and Abe and Ben each have $3$ times as much as Ceri.
            Together, Abe, Ben and Ceri have $3+3+1=7$ times as much as Ceri. So Ceri has
            $4354/7 = 622$ points.






            share|cite|improve this answer




















            • Thank you, I've been able to explain it to my daughter now (after learning myself!).
              – GrandMasterFlush
              Aug 26 at 20:12












            up vote
            3
            down vote



            accepted







            up vote
            3
            down vote



            accepted






            Let's remove $311$ points from Abe, without affecting Ben and Ceri. So now the total is $4665 - 311 = 4354$, and Abe and Ben each have $3$ times as much as Ceri.
            Together, Abe, Ben and Ceri have $3+3+1=7$ times as much as Ceri. So Ceri has
            $4354/7 = 622$ points.






            share|cite|improve this answer












            Let's remove $311$ points from Abe, without affecting Ben and Ceri. So now the total is $4665 - 311 = 4354$, and Abe and Ben each have $3$ times as much as Ceri.
            Together, Abe, Ben and Ceri have $3+3+1=7$ times as much as Ceri. So Ceri has
            $4354/7 = 622$ points.







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered Aug 26 at 19:58









            Robert Israel

            306k22201443




            306k22201443











            • Thank you, I've been able to explain it to my daughter now (after learning myself!).
              – GrandMasterFlush
              Aug 26 at 20:12
















            • Thank you, I've been able to explain it to my daughter now (after learning myself!).
              – GrandMasterFlush
              Aug 26 at 20:12















            Thank you, I've been able to explain it to my daughter now (after learning myself!).
            – GrandMasterFlush
            Aug 26 at 20:12




            Thank you, I've been able to explain it to my daughter now (after learning myself!).
            – GrandMasterFlush
            Aug 26 at 20:12










            up vote
            2
            down vote













            Let the scores be $A,B,C$ with the obvious notation. Then we have $$A+B+C=4665quad&quad B=A-311quad &quad B=3Cimplies$$ $$implies A+(A-311)+frac A-3113=4665$$



            Can you finish from here?






            share|cite|improve this answer


























              up vote
              2
              down vote













              Let the scores be $A,B,C$ with the obvious notation. Then we have $$A+B+C=4665quad&quad B=A-311quad &quad B=3Cimplies$$ $$implies A+(A-311)+frac A-3113=4665$$



              Can you finish from here?






              share|cite|improve this answer
























                up vote
                2
                down vote










                up vote
                2
                down vote









                Let the scores be $A,B,C$ with the obvious notation. Then we have $$A+B+C=4665quad&quad B=A-311quad &quad B=3Cimplies$$ $$implies A+(A-311)+frac A-3113=4665$$



                Can you finish from here?






                share|cite|improve this answer














                Let the scores be $A,B,C$ with the obvious notation. Then we have $$A+B+C=4665quad&quad B=A-311quad &quad B=3Cimplies$$ $$implies A+(A-311)+frac A-3113=4665$$



                Can you finish from here?







                share|cite|improve this answer














                share|cite|improve this answer



                share|cite|improve this answer








                edited Aug 26 at 20:02

























                answered Aug 26 at 19:57









                lulu

                36.2k14275




                36.2k14275



























                     

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