Question 155819
A candy company makes the popular Dandy Bar. The rectangular shaped bar is 10 centimeters long, 5 cm wide, and 2 cm thick. Because of increasing costs, the company has decided to cut the volume of the bar by a drastic 28%. The thickness will be the same, but the length and width will be reduced by equal amounts. What will be the length and width of the new bar?
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Let x = amount of reduction to length and width of candy bar
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Volume = length*width*thickness
Original volume = 10*5*2 = 100 sq cm
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Our equation, "28% reduction of volume":
(1-.28)(100) = (10-x)(5-x)2
(.72)(100) = (50-10x-5x+x^2)2
72 = 100-20x-10x+2x^2
72 = 2x^2-30x+100
0 = 2x^2-30x+28
0 = x^2-15x+14
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Factoring the right:
0 = (x-1)(x-14)
solutions x={1,14}
We can toss the 14 out since our length is only 10 cm subtracting by 14 will produce a negative number -- doesn't make sense.  So we MUST conclude that the only solution is x=1 cm
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Therefore, the conclusion is:
Original size of candy bar: 
10 cm (length)
5 cm (width)
2 cm (thick)
New size of candy bar:
10-1 = 9 cm (lenth)
5-1 = 4 cm (width)
2 cm (thick)
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Length of new candy bar: 9 cm
Width of new candy bar: 4 cm