# 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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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."
&Rightarrow;
3b=2+a

"Lengths are left--(3a-b) in. And right--(2+a+2b) in."
&Rightarrow;
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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