It should be clear that the goal is to reduce the area 12*7 = 84 cm^2 by 10%
by reducing the length of 12 cm to 12-x cm and reducing the width of 7 cm to 7-x cm.


It gives you an equation for the new area

    (12-x)*(7-x) = 0.9*84  cm^2,

or

    (12-x)*(7-x) = 75.6  cm^2


Simplify and reduce this equation to the standard queadratic equation form

    84 - 7x - 12x + x^2 = 78.6

    x^2 - 19x + 5.6 = 0.


Solve using the quadratic formula

     =  =  = .


Thus, one root is   =  = 18.70 cm.

The other root is   =  = 0.299 cm  (rounded).


Obviously, the first root is toooooo big value; so, we deny it.


Check the other root.  The new area is

    (12-0.299)*(7-0.299) = 78.41,


which is close to 78.4 = 0.9*84.


So, our solution is 0.299 cm.


The new dimensions are  12-0.399 = 11.601 cm (the length) and  7-0.399 = 6.601 cm (the width).    ANSWER

A jumbo chocolate bar with a rectangular shape measures 12 centimeters in length, 7 centimeters in width,and 3 centimeters in thickness.Due to escalating costs of cocoa,management decides to reduce the volume of the bar by 10%.To accomplish this reduction, management decides that the new bar should have the same 3 centimeter thickness,but the length and width of each should be reduced an equal number of centimeters. What should be the dimensions of the new candy bar?

I need help with this one. Too many words and numbers throw me into a loop. 

Volume of the OLD bar: Length * Width * Thickness = 12 * 7 * 3 = 252 cc
Volume of the NEW bar: (1 - .1)252 = .9(252) = 226.8 cc

Let reduction in length be r. Reduction in width is also r.
Thickness of NEW bar: 3
Length of NEW bar: Original length, less reduction, or 12 - r 
Width of NEW bar: Original width, less reduction, or 7 - r 

(Length of NEW bar) * (Width of NEW bar) * (Thickness of NEW bar) = (Volume of NEW bar)  
      (12 - r)      *       (7 - r)      *         (3)            =        226.8

3(12 - r)(7 - r) = 226.8
   

Solve using the quadratic equation formula: 

                                            , with: 
                                            
Reduction in original length and width, or  

                                            OR

Reduction in original length and width, or 


Dimensions of NEW bar: Thickness    x    Length    x     Width 
                                3        x (12 - .453)  x   (7 - .453)
                               3      x   11.547  x    6.547 = 226.795 cc (APPROXIMATELY 226.8 cc)