Question 1189654
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Tony and Peter both had some marbles at first. After Tony gave Peter 4/14 of his marbles, 
the ratio of Tony’s marbles to Peter’s marbles became 5:3. 
What was the ratio of Peter’s marbles to Tony’s marbles at first?.
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            For me,  it is psychologically difficult to see  (to read)  so long solution for so simple problem.


            So, I came to bring a shorter solution  (thinking that longer solution does not help understanding).



<pre>
Finally, Tony has 5x marbles, while Peter has 3x marbles, where x is the common measure.


Let P = # of marbles Peter had initially;

    T = # of marbles Tony  had initially.


Then we have these equations

    3x = P + {{{(4/14)*T}}}    (1)

    5x = {{{(10/14)*T}}}       (2)


From equation (2),  x = {{{(5/7)*(1/5)*T}}} = {{{(1/7)*T}}}.


Substitute it into equation (1) to get

    {{{(3/7)T}}} = P + {{{(2/7)*T}}}.


So,  P = {{{(3/7)*T}}} - {{{(2/7)*T}}} = {{{(1/7)*T}}}.


It means that  {{{P/T}}} = {{{1/7}}}.     <U>ANSWER</U>
</pre>

Solved.



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My conception is this: everything which is longer than 5 lines of standard text, is not a Math problem.


If a standard/regular school Math problem is given, than its solution should be no longer than 10 - 15 lines of the text; maximum 20 lines.


If a problem is exceptional, its solution may require "more lines" - it depends and it can be justified.


But if the solution to a regular/standard school Math problem is longer than 20 lines, then nobody even will read it . . .