Question 1183630
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A marketing manager for a publishing company has a 6 foot by 8 foot banner to be used when setting up 
booths at educational conferences. She decides add more zing to the booth by increasing the square footage by 50%, 
and plans to accomplish this by increasing each of the dimensions by the same amount. What will the new dimensions be?
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After adding x to old dimension, the new dimensions are (6+x) ft and (8+x) ft.


The new area is 50% more than the old area, which was 6*8 = 48 ft^2.


So, the new area is 48 + 0.5*48 = 72 ft^2,  giving the equation


    (6+x)*(8+x) = 72.


Simplify and find x


    48 + 6x + 8x + x^2 = 72

    x^2 + 14x - 24 = 0


It is not factorable, so use the quadratic formula


    {{{x[1,2]}}} = {{{(-14 +- sqrt(14^2 + 4*24))/2}}} = {{{(-14 +- sqrt(292))/2}}}.


Of the two roots, select only the positive root as the solution to the problem


    x = {{{(-1 + sqrt(292))/2}}} = 1.544 ft  (rounded).    <U>ANSWER</U>


<U>ANSWER</U>.  New dimensions are  6+1.544 = 7.544 ft  and  8+1.544 = 9.544 ft.


<U>CHECK</U>.  7.544*9.544 = 71.99994  ft^2.    ! Good ;  Correct !
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Solved.