Question 224248
The length of a rectangle is increased by 120% and its width is decreased by 20%, what is the resulting percentage increase or decrease in the area? Justify your answer algebraically.


Step 1.  120% means 1.2 and 20% means 0.20


Step 2.  Let L be the original length and 1.20L be the increased length.


Step 3.  Let w be the original width and (1-0.2)w=0.8w be the reduced width.


Step 4.  Let w*L be the original area.


Step 5.  Then, (0.8w)*(1.20L)=0.96w*L = (1-0.04)w*L


Step 6.  ANSWER:  The area is 96% of the original area or the area is reduced by 4%.


I hope the above steps were helpful.


For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


Good luck in your studies!


Respectfully,
Dr J