Question 165522: Please tell me how to do this problem (step-x-step). I just don't get these and I really want to understand what I'm doing. The instructor also gave a way to use the TI-83 for solving but I couldn't follow him.
The length of a rectangular box is 1 inch more than twice the height of the box, and the width is 3 inches more than the height. If the volume of the box is 126 cubic inches, find the dimensions of the box.
Thanks for taking the time to help me.
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! volume = length times width times height.
let V = volume
let L = length
let W = width
let H = height
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V = L * W * H (equation 1)
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The length of a rectangular box is 1 inch more than twice the height of the box.
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L = 2 * H + 1 (equation 2)
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the width is 3 inches more than the height.
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W = H + 3 (equation 3)
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the volume of the box is 126 cubic inches.
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V = 126 cubic inches.
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you start with equation 1
V = L * W * H (equation 1)
you use equation 2 and equation 3 to substitute for W and L.
L = 2 * H + 1 (equation 2)
W = H + 3 (equation 3)
equation 1 becomes:
V = (2 * H + 1) * (H + 3) * H
126 = (2*H+1)*(H+3)*H
this becomes
2h^3 + 7h^2 + 3h - 126 = 0
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i couldn't solve it so i went to an online calculator and asked it to do the dirty work for me.
first calculator i went to couldn't handle it, but the second calculator i went to did.
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the real solution (there were others but they were complex (real + imaginary)) was h = 3.
i plugged that into the equation and it proved to be good.
i used H = 3 and went back to equations 2 and 3 to get the values for L and W.
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H = 3
L = 2 * H + 1 (equation 2)
W = H + 3 (equation 3)
from equation 2:
L = 7
from equation 3:
W = 6
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dimension are:
L = 7
W = 6
H = 3
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V = 126
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V = L*W*H
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L*W*H = 126
7*6*3 = 126
126=126
answer is good.
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sorry i can't help you with the TI-83.
if you want to us an online calculator, this is the one that solved the equation for me.
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http://www.ifigure.com/math/algebra/algebra.htm
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i clicked on "equations" in the solving equations section.
then i clicked on "go to the solve page" in the solve section.
then i entered my equation and i told it the letter i wanted it to solve for (h in my case), and it gave me the solutions.
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