SOLUTION: Below is a floor plan for a combined living and dining area. The owners of the home have recently adopted a puppy, so the living room needs to be re-carpeted (bad puppy). The t

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Below is a floor plan for a combined living and dining area. The owners of the home have recently adopted a puppy, so the living room needs to be re-carpeted (bad puppy). The t      Log On

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Question 1155186: Below is a floor plan for a combined living and dining area. The owners of the home have recently adopted a puppy, so the living room needs to be re-carpeted (bad puppy).
The total area for both rooms is expressed as: 2x^2+x+3 square meters. The tile in the dining room was already replaced, so we know the area of that room is: 2x^2-2x square meters.
Known area of dining room: 2x^2-2x square meters.
Area of combined dining and living room: 2x^2+x+3 square meters.
Find an expression for the area that needs to be re-carpeted.
After solving, choose the expressions that represent the length and width of the dining room, which can be found by completely factoring its area.
2x meters
(x-1) meters
(x+1) meters
x meters
(2x-2) meters
2 meters

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The total area for both rooms is expressed as:
living and dining area
2x%5E2%2Bx%2B3 square meters.
The tile in the dining room was already replaced, so we know the area of that room is: 2x%5E2-2x square meters.
Known area of dining room:+2x%5E2-2x square meters.
so, subtract the dining room from the total area of living and dining area
2x%5E2%2Bx%2B3-%282x%5E2-2x%29
2x%5E2%2Bx%2B3-2x%5E2%2B2x
3x%2B3
Area of combined dining and living room:
2x%5E2%2Bx%2B3 square meters
the area that needs to be re-carpeted is
2x%5E2%2Bx%2B3-%283x%2B3%29
2x%5E2%2Bx%2B3-3x-3
2x%5E2-2x
the living room area that needs to be re-carpeted is :
2x%5E2-2x........factor it
2x%28x-1%29
the length of the dining room is 2x and width is x-1