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

Algebra ->  Customizable Word Problem Solvers  -> Misc -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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(22740) About Me  (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:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation: a=3; b=-57; c=50.5
x+=+%28-%28-57%29+%2B-+sqrt%28-57%5E2+-+4%2A3%2A50.4+%29%29%2F%282%2A3%29+
:
x+=+%2857+%2B-+sqrt%283249+-+604.8+%29%29%2F%286%29+
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