Help with expression word problems please?
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Help with expression word problems please?

[From: ] [author: ] [Date: 14-02-13] [Hit: ]
............

Area of tiled portion or room = 10(25) = 250 m^2..........ANS

Area of the entire room = (2w+25)(2w+10)
.......................................... 4w^2 + 20w + 50w + 250
.......................................... 4w^2 + 70w + 250..................ANS

Area of the wood frame = 2(25w) + 2(10w) + 4(w^2)
.......................................... 4w^2 + 70w

Owners can only afford 74 m^2 of wood so
4w^2 + 70w = 74
4w^2 + 70w - 74 = 0

...........-70 ±√(70^2 - 4(4)(-74))
w = -----------------------------------
...........................2(4)

...........-70 ± 78
w = ----------------
.................8


w = 1, or -18.5 but you can't have a negative length so the answer is simply

w = 1......................................A...

-
1.) Area = A

A = (3x - 1)(2x + 2)

Expanding,

A = 6x² + 6x - 2x - 2
A = 6x² + 4x - 2

Answer: 6x² + 4x - 2 sq. m.
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2.) A = x² - x - 2

Factoring,

A = (x - 2)(x + 1)

Answer: (x + 1)
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3.) Area of Dining Room, Ad = 2x² - 2x
Area of Combined Space, Ac = 2x² + x + 3
Area of Living Room = Al

Al = Ac - Ad

Subbing known values,

Al = 2x² + x + 3 - (2x² - 2x)
Al = 2x² + x + 3 - 2x² + 2x
Al = 2x² - 2x² + x + 2x
Al = x + 2x
Al = 3x

Answer: 3x meters
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4.) Length of Tiled Floor, Lt = 25 m.
Width of Tiled Floor, Wt = 10 m.
Width of Border = w
Length of Entire Floor Space = Le
Width of Entire Floor Space = We

Le = 2w + Lt

Subbing,

Le = 2w + 25


We = 2w + Wt

Subbing,

We = 2w + 10

Answer:

Length of Entire Room = 2w + 25
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Width of Entire Room = 2w + 10
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