<PRE><B>Question 1172184</B>
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(1) If an algebraic solution is required, I suggest using a single variable, instead of using two variables and then doing substitution to obtain a single equation in one variable.&lt;br&gt;
Furthermore, since the area given is of the painting plus border, use the length and width of the painting plus border in your equation, then subtract the border to get the answer (the dimensions of the painting without the border).&lt;br&gt;
x = length (inches) (painting plus border)
x-3 = width (3 inches less than the length)&lt;br&gt;
The area of the painting plus border (length times width) is 108 square inches:&lt;br&gt;
{{{x(x-3) = 108}}}
{{{x^2-3x = 108}}}
{{{x^2-3x-108 = 0}}}
{{{(x-12)(x+9) = 0}}}
{{{x = 12}}} OR {{{x = -9}}}&lt;br&gt;
Select the positive solution, since negative numbers don&#39;t make sense for lengths.&lt;br&gt;
The length of painting plus border is x=12 inches; the width is 9 inches.&lt;br&gt;
Subtract 2 inches from each dimension to get the dimensions of the painting without the 1-inch border.&lt;br&gt;
ANSWERS: The length of the painting is 12-2=10 inches; the width is 9-2=7 inches.&lt;br&gt;
Note that the formal algebra didn&#39;t get you any closer to the answer -- to solve the quadratic equation, you had to find two numbers whose difference is 3 and whose product is 108.  But that&#39;s what the original problem asked you to do....&lt;br&gt;
So the quick and easy mental solution is to find that 12-9=3 and 12*9=108, which means the dimensions of the painting plus border are 12 by 9, making the dimensions of the painting 10 by 7.&lt;br&gt;
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