SOLUTION: The length of a rectangle is two feet more than three times the width. Express as an integer the maximum width of the rectangle when the perimeter is less than twenty-eight feet.

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Question 101805: The length of a rectangle is two feet more than three times the width. Express as an integer the maximum width of the rectangle when the perimeter is less than twenty-eight feet.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
L – Length
W – Width
From your explanation,
L = 2 + 3W
The perimeter,P, of a rectangle is the sum of twice the width and twice the length or P=2L+2W.
P = 2L + 2W
P = 2(2+3W) + 2W Substitute from above for L.
P = 2(2)+ 2(3W)+ 2W Distributive Property.
P=4+6W+2W Simplify.
P=4+8W
From your explanation, the perimeter must be less than 28 feet or P<28 ft.
P<28
4+8W<28 Substitute.
4-4+8W<28-4 Additive inverse of 4 or (-4).
8W<24
8W/8<24/8 Multiplicative inverse of 8 or (1/8)
W<3
Since W is less than 3 and must be an integer, then the maximum value it can have is 2.
W=2 ft.