SOLUTION: 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

Question 155819This question is from textbook
: 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? This question is from textbook

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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?
.
Let x = amount of reduction to length and width of candy bar
.
Volume = length*width*thickness
Original volume = 10*5*2 = 100 sq cm
.
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
.
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
.
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)
.
Length of new candy bar: 9 cm
Width of new candy bar: 4 cm

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