Question 1173010
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    Bianca  +  Father    = 109    (in total)


      B     +  (3B + 13) = 109


      B     + 3B   + 13  = 109


         4B              = 109 - 13

         4B              = 96

          B              = 96/4 = 24.


<U>ANSWER</U>.  Bianca picked 24 apples.  The father picked 3*24 + 13 = 85 apples.


<U>CHECK</U>.  24 + 85 = 109, in total.   ! Precisely correct !
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Solved.


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Which approach to use - one equation or two equations ? ? ?


It mostly depends on the age, level/grade and readiness of the student . . . 


Young students may not know systems of two equations - - - then only one equation approach does work.


As the student becomes older, he (or she) is able to adopt the two equations approach.


I always try to guess from the context, which age and which level the student is - and react accordingly.


A mature student, ideally, should know both approaches; freely manipulate with either approach 
and understand when and why they both are equivalent.


Then the issue on which approach to use is only the question of taste and traditions . . . 



With two small additions.


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1.  One equation approach gives the opportunity for earlier education and 

    earlier involvement of a young student to problems solving - - - comparing with the two-equation approach.



2.  There is a class of problems, which are, from the first glance, for 3-equation approach,

    but actually can be easily solved using 1-equation approach.


    For this class of problems, it is CONCEPTUALLY IMPORTANT to teach young students to make right setup.

    It is the moment, when right teaching really helps to built young minds in a right way.
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