Question 149810
Let x=width of border.


First, let's draw the picture. 


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/rectangle2.png" alt="Photobucket - Video and Image Hosting">


note: the lengths {{{40-2x}}} and {{{30-2x}}} are due to the subtraction of 2 "x" lengths. Take note that there are two dashed lines per side that are not part of the green tiles.



From the picture, we see that the actual counter top is {{{40-2x}}} by {{{30-2x}}}. So the length is {{{L=40-2x}}} and the width is {{{W=30-2x}}}



Now remember, the area of a rectangle is 


{{{A=L*W}}}


{{{704=(40-2x)(30-2x)}}} Plug in the given area of the green tiles {{{A=704}}}, {{{L=40-2x}}} and {{{W=30-2x}}}



{{{704=1200-140x+4x^2}}} FOIL



{{{0=1200-140x+4x^2-704}}} Subtract 704 from both sides.



{{{0=4x^2-140x+496}}} Combine like terms.



Let's use the quadratic formula to solve for x



{{{x = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{x = (-(-140) +- sqrt( (-140)^2-4(4)(496) ))/(2(4))}}} Plug in  {{{a=4}}}, {{{b=-140}}}, and {{{c=496}}}



{{{x = (140 +- sqrt( (-140)^2-4(4)(496) ))/(2(4))}}} Negate {{{-140}}} to get {{{140}}}. 



{{{x = (140 +- sqrt( 19600-4(4)(496) ))/(2(4))}}} Square {{{-140}}} to get {{{19600}}}. 



{{{x = (140 +- sqrt( 19600-7936 ))/(2(4))}}} Multiply {{{4(4)(496)}}} to get {{{7936}}}



{{{x = (140 +- sqrt( 11664 ))/(2(4))}}} Subtract {{{7936}}} from {{{19600}}} to get {{{11664}}}



{{{x = (140 +- sqrt( 11664 ))/(8)}}} Multiply {{{2}}} and {{{4}}} to get {{{8}}}. 



{{{x = (140 +- 108)/(8)}}} Take the square root of {{{11664}}} to get {{{108}}}. 



{{{x = (140 + 108)/(8)}}} or {{{x = (140 - 108)/(8)}}} Break up the expression. 



{{{x = (248)/(8)}}} or {{{x =  (32)/(8)}}} Combine like terms. 



{{{x = 31}}} or {{{x = 4}}} Simplify. 



So the possible answers are {{{x = 31}}} or {{{x = 4}}} 



However, we need to see if they generate reasonable lengths and widths



Let's check the solution {{{x = 31}}}



{{{L=40-2x}}} Go back to the length equation



{{{L=40-2(31)}}} Plug in {{{x = 31}}}



{{{L=40-62}}} Multiply



{{{L=-22}}} Subtract



Since a negative length is not possible, this means that the value  {{{x = 31}}} is a reasonable solution.



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Let's check the solution {{{x = 4}}}



{{{L=40-2x}}} Go back to the length equation



{{{L=40-2(4)}}} Plug in {{{x = 4}}}



{{{L=40-8}}} Multiply



{{{L=32}}} Subtract

  
So we get a reasonable length with {{{x = 4}}}


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{{{W=30-2x}}} Go back to the width equation



{{{W=30-2(4)}}} Plug in {{{x = 4}}}



{{{W=30-8}}} Multiply



{{{W=22}}} Subtract

  
So we also get a reasonable width with {{{x = 4}}}



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Answer:


So the only solution is {{{x = 4}}}



So the width of the border is 4 inches