Question 1210613
DATA WE HAVE:
Marek and Zaven had 900 coins altogether.
That is what they had initially.
 
Zaven was left with 50% (half) as many coins as the number he spent.
He spent twice as many coins as he was left with. 
For every 1 coin he had left, there were 2 he had spent, and 3 that he originally had.
That tells me that the number of coins Zaven initially had was a multiple of 3.
 
Marek spent 25% fewer coins than Zaven.
Marek spent 100%-25%=75% of what Zaven spent.
If I knew how much Zaven spent I can multiply times 0.75 to find what Marek spent. 
For every 4 coins Zaven spent Marek spent 3. So I could instead divide by 4 and multiply times 3.
  
Marek had 75% of the total number of coins the two friends had left in the end.
 
Could Marek have initially had 75% of the total number of coins the two friends had left in the end? It does not seem possible.
I think what the "in the end" part applies to the whole sentence, and what was meant is:
In the end, Marek had 75% of the total number of coins the two friends had left.
 
AN EASY WAY TO SOLVE IT (guess and check):
 
Fist Guess:
What if Zaven initially had {{{300coins}}}.
Then, Zaven must have spent {{{200coins}}} ,
and must have had left with {{{300coins-200coins=100coins}}} in the end.
Then, Marek
must have started with {{{900coins-300coins=600coins}}}
must have spent {{{0.75*200coins=150coins}}} ,
and have had left {{{600coins-150coins=450coins}}} in the end.
Then, Zaven and Marek then together had {{{100coins+450coins=550coins}}} in the end,
and that would mean that in the end,
the number of coins Marek had,
as a fraction and as a percentage of the number of coins Zaven and Marek had together, was
{{{450coins/"550 coins"=9/11="0.818181..."="81.8181..."}}}{{{"%"}}}
 
We need {{{75}}}{{{"%"}}} as an answer, so we should try to have Marek start with a little less with respect to Zaven.
 
second Guess:
What if Zaven initially had {{{360coins}}}.
Then, Zaven must have spent {{{240coins}}} ,
and must have had left with {{{360coins-240coins=120coins}}} in the end.
Then, Marek
must have started with {{{900coins-360coins=540coins}}}
must have spent {{{0.75*240coins=180coins}}} ,
and have had left {{{540coins-180coins=360coins}}} in the end.
Then, Zaven and Marek then together had {{{120coins+360coins=480coins}}} in the end,
and that would mean that in the end,
the number of coins Marek had,
as a fraction and as a percentage of the number of coins Zaven and Marek had together, was
{{{360coins/"480 coins"=3/4=75/100=0.75=75/100=75}}}{{{"%"}}}
 
A HYBRID OF THE SOLUTION ABOVE AND jogsarithmetic's solution:
Let's call the number of coins Zaven had at start, what he spent, and what he had left in the end 3x, 2x, and x, respectively.
{{{matrix(4,4," ",Zaven,Marek, Zaven + Marek,
initially,3x,900-3x,900,
spent,2x,1.5x,3.5x,
final,x,900-4.5x,900-3.5x)}}}
Then, we have just one variable, and the equation
{{{(900-4.5x)/(900-3.5x)=0.75}}}<-->{{{900-4.5x=0.75(900-3.5x)}}}<-->{{{3600-18x=3(900-3.5x)}}}<-->{{{3600-18x=2700-10.5x}}}<-->{{{3600-2700=7.5x)}}}
{{{x=900/7.5=120}}}
In th e end, the number of coins Marek had was {{{900-4.5*120=900-540=highlight(360)}}}
 
Some teachers want problems solved the way it was taught in class, and may not like alternative solutions.
Some teacher may want to give extra point f=if more that one way to solve the problem is shown.