SOLUTION: A business is expanding a 7’ by 21’ storage area by adding x feet to the width and three times x to the length. The change will increase the area by 153 square feet. What is th

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A business is expanding a 7’ by 21’ storage area by adding x feet to the width and three times x to the length. The change will increase the area by 153 square feet. What is th      Log On


   

Question 1154159: A business is expanding a 7’ by 21’ storage area by adding x feet to the width and three times x to the length. The change will increase the area by 153 square feet. What is the value of x?
Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
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New dimensions are (7+x) feet by (21+3x) feet.


The change in the area is  (7+x)*(21+3x) - 7*21 square feet.


The change is equal to 153 square feet. It gives an equation


    (7+x)*(21+3x) - 7*21 = 153.


Simplify and solve for x.


    7*21 + 21x + 21x + 3x^2 - 7*21 = 153

    3x^2 + 42x - 153 = 0.

     x^2 + 14x - 51 = 0

     (x - 3)*(x+17) = 0


From two roots, 3 and -17, we should choose the positive value x= 3.


ANSWER.  x= 3.


CHECK.  10*30 - 7*21 = 153.   ! Precisely correct !

Solved.