Question 1208344
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Alan Ben and Caleb shared some marbles. Alan took 40% of the marbles and was given 1 more . 
Ben took 25% of the remaining and was given 3 more. 
Caleb took the remaining 12 marbles. How many were there at first.
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<pre>
Let T be the total number of marbles.


Alan has 0.4T +1 marbles;  the remaining is T - (0.4T+1) = 0.6T-1.

Ben has 0.25(0.6T-1) + 3 marbles;

Caleb has 12 marbles.


Write an equation for the total

    (0.4T + 1) + (0.25(0.6T-1) + 3) + 12 = T.


Simplify and find T

    0.4T + 1 + 0.15T - 0.25 + 3 + 12 = T

    0.55T + 15.75 = T

    15.75 = T - 0.55T

    15.75 = 0.45T

     T = 15.75/0.45 = 35.


<U>ANSWER</U>.  The total number of marbles is/was 35.

          This total number of marbles was not changed before and after: it remained THE SAME.
</pre>

Solved.


The question in the problem is posed INCORRECTLY.


The correct question is: "How many marbles were there in total ?"



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Let me explain you, WHY I think that the question is posed incorrectly
and WHY a TRUE question should be posed differently.


In this problem, the marbles were distributed inside some group of three people.
No marbles went outside. Therefore, the total number of marbles at the beginning was  
the same as at the end.  So, there is a hidden symmetry between the future and the past
in this problem. The symmetry is that the number of the marbles at the origin
and at the end is the same.


If the problem's creator  formulates the problem according to my instruction, he (or she) 
demonstrates that he/she recognizes this symmetry and does not violate it.  
If he/she formulates differently, he/she demonstrates that he/she does not care 
about his/her language and leaves to the reader to figure out these details on his/her own. 
My point is that the problem should sound harmonically, should be posed clearly 
and should not distract the reader from the essence of the task.


That's all. 


Behind all this is respect / (or disrespect) for the symmetry, for the harmony and for the reader.


Nothing more and nothing else.