posted by HM on .
A box with no top is to be constructed from a piece of cardboard whose Width measures x inch
and whose length measures 3 inch more than the width
the box is to be formed by cutting squares that measure 1 inch on each side of the 4 corners and then folding up the sides
If the volume of the box is 180 inch then what are the dimensions
Now I am trying to solve it through
Volume=L * W * Height
Length = 3+x
Width = x
and Volume 180 inch
An answer-er came up with this solution>
If you make a sketch you will see that the
length = 3+x - 2 = x+1
and the width is
the height will be 1
Volume = (x+1)(x-2)(1) = 180
x^2 - x - 2 - 180 = 0
x^2 - x - 182 = 0
(x-14)(x+13) = 0
x = 14 or x = -13, but clearly x > 0
box is x+1 by x-2 by 1
15 by 12 by 1
check: what is 15*12*1 ?
is the length of 15 greater than the width of 12 by 3 ?
It is wrong the multiple choices for this question are >>>
1. 17 inch by 14 inch
2. 21 inch by 18 inch
3. 20 inch by 17 inch
and non of them match up to his answer..
WHERE ARE WE GOING WRONG?
HM -- Since you've chosen not to post your choices, then I don't think you're serious about finding the correct answer.
I wrote the choice, the answer I am getting is 15inch by 12 too. :/
I had answered this for you, and you included my solution in your post above
You agreed that the answer was correct.
I verified my answer.
Since that answer is not included in their choices, we must reach the "inescapable conclusion" that they are wrong.
Yes I thanked you Reiny and I tried to use your method too !
However I keep coming to the same conclusion thus I put it as my answer too.
But I am thinking there must be a solution to this, MATHLAB can not be wrong.
I will get back to you with this.
I think I can see where the problem arises.
I found 15 and 12 to be the dimensions of the box.
Which means that the size of the original piece of carboard was 17 by 14, (remember 1 inch is removed on both ends)
Their question was ...
"If the volume of the box is 180 inch then what are the dimensions"
Grammatically, the "dimensions" must refer to the box.
So try 17 by 14 , the size of the cardboard.
You could be right ! Perhaps we did not have to minus the width and the length from 1 which gives us.
And then we place in the values of 14 only since -13 is not counted.
and then we
3+14 > 17
and x = 14
which gives us 17 inch to 14.
But wait how did we get the 14 and -13 since the answers to 3x^2+3x-180=0 are different...
Ignoring the fact that their question is poorly worded, it all makes sense.
width = x
length = x+3 ---- that was given
length = (x+3) - 2 = x+1
width = x-2
height = 1
vol = 1(x-2)(x+1)
= x^2 - x - 2
so x^2 - x - 2 = 180
x^2 - x - 182 = 0
(x-14)(x+13) = 0
x = 14 , and we ignore the other negative answer.
So original cardboard is x by x+3 or 14 by 17
dimensions of box : x-2 by x+1 or 12 by 15
So it depends what we are answering.
How did you ever come up with the equation 3x^2 + 3x - 180 = 0 ????
Thank you Reiny ! I very much understand what is going on now !
These kinds of questions are easy but the wordings always trick you.
I came up with 3x^2+3x-180=0
through this (3+x)(x)=180
I guess we figure out the dimensions of the cardboard and then the dimensions of the box right?
I hope you see that the equation 3x^2 + 3x - 180 = 0 does not fit in here at all
since x was the original width of the cardboard
and x+3 was the original length
x(x+3) = 180 would be saying:
the AREA of the cardboard is 180
The question is really confusing now..
The equation for the dimensions are different and we calculate the x in a different way?
From what I see you are saying :
the equation of the box is (x)(x+3)=180
when this is put into a Quadratic equation this gives us -15, 12
12 is considered.
but then when 12 is put in there it gives us the dimensions are 12inch and 15inch
However we must add the +2 to both since we did not measure the -1 taken on all 4 sides right.
Btw that is my brother. He is trying to help me out too.
It is asking for the dimensions of the piece of cardboard !
You are absolutely right, we first find the box's dimensions and then we ADD 2 to each side to get the dimension of the cardboard !