Let the original area = A, the original length be L,
and the original width be W.
 
Then 

OLD AREA = (OLD LENGTH)(OLD WIDTH), so we have this
equation:



The new area = , because it was doubled.

The new length = , because 50% or half of L 
was added to L.

We don't know what the width is multiplied by, so let's suppose
it was multiplied by some number k, making the new width kW

Then the new rectangle's area is given by:

NEW AREA = (NEW LENGTH)(NEW WIDTH)
       
      
      
      
Clear of fractions by multiplying both sides by 2:
      
      
       
      
      
So we have the system of equations:



Now let's divide equals by equals:



We cancel:

 





So the width was multiplied by  so it was
increased by  or 

Edwin