<PRE><B>Question 1149545</B>
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Corrected response... sorry for the brain freeze in the original&lt;br&gt;
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You should know how to set up a problem like this for solving using formal algebra, so let&#39;s do that.&lt;br&gt;
Let the width of the border by x.  Then the dimensions of the finished product are 11+2x and 17+2x.  So we need to find the value of x for which (11+2x) times (17+2x) is equal to 315.&lt;br&gt;
{{{(2x+11)(2x+17) = 4x^2+56x+187 = 315}}}
{{{4x^2+56x-128 = 0}}}
{{{x^2+14x-32 = 0}}}&lt;br&gt;
To solve from here, we need to factor that quadratic, by finding two numbers whose product is 32 and whose difference is 14.&lt;br&gt;
{{{(x+16)(x-2) = 0}}}
{{{x = -16}}} or {{{x = 2}}}&lt;br&gt;
Clearly the negative answer makes no sense in the problem, so we choose the positive solution.&lt;br&gt;
ANSWER: The width of the border is x=2 inches.&lt;br&gt;
So with the algebraic solution, we end up having to find two numbers with a product of 32 and a difference of 14.&lt;br&gt;
But the original problem asks us to find two numbers with a product of 315 and a difference of 17-11 = 6.&lt;br&gt;
So the formal algebraic solution doesn&#39;t simplify the task of finding the answer to the problem; it leads us to the same kind of task as the original problem.&lt;br&gt;
So if a formal algebraic solution is not required, we might as well solve the original problem directly.&lt;br&gt;
The prime factorization of 315 is 3*3*5*7.  We need to combine those factors into two numbers with a difference of 6.  A little trial and error leads us to 15*21; since the original dimensions were 11 and 17, twice the width of the border is 4 inches, so the width of the border is 2 inches.&lt;br&gt;
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