# 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, manageme

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 Question 161914: 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 20%. To accomplish this reduction, management decides that the new bar should have the same 3 centimeters 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?Answer by ankor@dixie-net.com(15667)   (Show Source): You can put this solution on YOUR website!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 20%. To accomplish this reduction, management decides that the new bar should have the same 3 centimeters 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? : Find the original volume of the bar 12 * 7 * 3 = 252 cu/cm : Reduced volume bar .8 * 252 = 201.6 cu/cm; (reduced by 20%) : Let x = no. of cm that length and width will be reduced : (12-x) * (7-x) * 3 = 201.6 FOIL (84 - 12x - 7x + x^2) * 3 = 201.6 : 3(x^2 - 19x + 84) = 201.6 : 3x^2 - 57x + 252 - 201.6 = 0 : 3x^2 - 57x + 50.4 = 0 : Use the quadratic formula to find x: In this equation: a=3; b=-57; c=50.5 : Do the math here and you will get two solutions, but the one that makes sense: x = .9297 cm : Reduce the length and width by this amt : 12-.9297 = 11.0703 cm is the new length 7 -.9297 = 6.0703 cm is the new width : Check solution by finding the volume of the the new bar 11.0703 * 6.0703 * 3 = 201.6, the required volume