SOLUTION: 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

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Question 1207438: 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.
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52855) (Show Source):
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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

Solved, with complete explanations.

Answer by MathTherapy(10556) (Show Source):
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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)