SOLUTION: 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 algebraical

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.
Found 2 solutions by drj, MathTherapy:
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
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

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
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.

Area of a rectangle = LW

If area is increased by 120%, then its new length is: 220% * L = 2.2L

Since its width is decreased by 20%, then its new width is: 80% * W = .8W

This makes its new area: 2.2L * .8W = 1.76LW

The difference in the original and new area is an increase of: 1.76 - 1, or .76

Therefore, the increase in its area is: = %
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