Question 1207438
<pre>
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
   {{{matrix(5,3, (3(12 - r)(7 - r))/3, "=", 226.8/3, (12 - r)(7 - r), "=", 75.6, 84 - 19r + r^2, "=", 75.6, r^2 - 19r + 84 - 75.6, "=", 0, r^2 - 19r + 8.4, "=", 0)}}}

Solve using the quadratic equation formula: {{{matrix(1,3, r, "=", (- b +- sqrt(b^2 - 4ac))/(2a))}}}

                                            {{{matrix(1,3, r, "=", (- (- 19) +- sqrt((- 19)^2 - 4(1)(8.4)))/(2(1)))}}}, with: {{{matrix(3,3, a, "=", 1, b, "=", - 19, c, "=", 8.4)}}}
                                            {{{matrix(3,3, r, "=", (19 +- sqrt(361 - 33.6))/2, r, "=", (19 +- sqrt(327.4))/2, r, "=", (19 +- 18.094)/2))}}}
Reduction in original length and width, or {{{matrix(1,9, r, "=", (19 + 18.094)/2, "=", 37.094/2, "=", 18.547, cm, highlight(matrix(1,4, "(IGNORE:", LARGER, than, "BOTH)")))}}} 

                                            OR

Reduction in original length and width, or {{{highlight_green(matrix(1,7, highlight(r), "=", (19 - 18.094)/2, "=", .906/2, "=", highlight(matrix(1,3, .453, cm, "(APPROXIMATELY)"))))}}}


<font color = blue><font size = 4><b>Dimensions of NEW bar:</font></font></b> Thickness    x    Length    x     Width 
                                3        x (12 - .453)  x   (7 - .453)
                           <font color = blue><font size = 4><b>    3      x   11.547  x    6.547</font></font></b> = 226.795 cc (APPROXIMATELY 226.8 cc)</pre>