Algebraic equations real life problems

A book cover has the length and width(in inches) shown in the diagram.
A) Find the values of a and b
B) Find the perimeter of the book cover.
Widths are top--3b in. bottom--(2+a)in.
Lengths are left--(3a-b) in. And right--(2+a+2b) in.

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asked by Logan
  1. as you know, perimeter is 2(length+width)

    With no actual numbers provided, it is impossible to assign values to a and b.

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    posted by Steve
  2. "Widths are top--3b in. bottom--(2+a)in."
    ⇒
    3b=2+a

    "Lengths are left--(3a-b) in. And right--(2+a+2b) in."
    ⇒
    3a-b=2+a+2b

    Solve for a and b, hence perimeter.
    Hint: both a and b are positive, and are both integers.

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  3. You have your two equations.

    3b = 2+a
    3a-b = 2+a+2b

    rearrange things a bit and you have

    a - 3b = -2
    2a - 3b = 2

    subtract and you have
    a=4
    so, b=2

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    posted by Steve

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