Question

A jumbo chocolate bar with a rectangular shape measures 12 centimeters in length, 8 centimeters in width, and 2 centimeters in thickness. Due to escalating costs of cocoa, the management has decided to reduce the volume of the bar by 10 %. To accomplish this reduction, management decides that the new bar should have the same 2 centimeter thickness, but the length and width of each should be reduced by an equal number of centimeters. What should be the dimensions of the new candy bar?

Answer 1

Original Volume of the chocolate bar: 12*8*2 = 192cm³

Volume 10% reduced will be: 172.8 cm³

The thickness has to remain 2 cm and the other ones must be reduced by an equal number of cm, so:

(12-x)*(8-x)*2 = 172.8

(12-x)*(8-x) = 86.4

96-12x-8x+x²-86.4 = 0

x²-20x+ 9.6 = 0

Now let's solve the quadratic equation:

$\begin{gathered} x²-20x+9.6=0 \\ \\ x=\frac{20\pm\sqrt{400-4*1*9.6}}{2} \\ \\ x=\frac{20\pm19.1}{2} \\ \\ x=0.45 \end{gathered}$

New dimensions:

12-0.45 = 11.55

8-0.45 = 7.55

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