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The root numbers in toothpaste (help)

  1. Feb 20, 2007 #1
    Pardon me for not using latex.
    1. The problem statement, all variables and given/known data
    A toothpaste box has square ends. The length is 12cm greater than the width. The volume of the box is 135cm^3. What are the dimensions of the box?


    2. Relevant equations
    Quadratic theory, Random pluggin for x, common factoring, Family of functions, graph


    3. The attempt at a solution
    Okay, i need 3 numbers when multiplied, will give me 135...
    5 into 135 = 27 into 3 times 3 times 3 = 27
    okay, good.
    and now I'm stuck
     
  2. jcsd
  3. Feb 20, 2007 #2

    cristo

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    Can you use this condition to set up an equation for, say, x; the sides of the square end?
     
  4. Feb 20, 2007 #3
    Alright im not so stuck anymore, here we go:
    V=LWH
    135=L(L-12)H
    Does this seem right?
     
    Last edited: Feb 20, 2007
  5. Feb 20, 2007 #4
    Well, you have two variables and only one equation.
    *edit* where is the 15 on the r.h.s. coming from?
     
  6. Feb 20, 2007 #5

    cristo

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    No, where does 15 come from?

    The simplest way is to take w, say, as the width of the box(note, this is also the height, since the ends are square). Then, the length l, say, is 12 cm greater than w. So, can you express l in terms of w? Then, your formula v=lwh=135 is correct, so substitute into this (again, noting that w=h).
     
  7. Feb 20, 2007 #6
    Edited... width is 12 cm less than Length
     
  8. Feb 20, 2007 #7
    okay, now how is the width related to the height?
     
  9. Feb 20, 2007 #8
    A toothpaste box has square ends. The length is 12cm greater than the width. The volume of the box is 135cm^3. What are the dimensions of the box?
     
  10. Feb 20, 2007 #9
    The ends are square, which I think you are denoting each side of the square as height and width. Now the two sides of a square are____?
     
  11. Feb 20, 2007 #10
    You Smart Little .... Ugh Why am i so Blind.... WOW!!
     
  12. Feb 20, 2007 #11
    I am blind too, just spent more time in this darkness!
     
  13. Feb 20, 2007 #12
    You have the width listed as w. The length is listed as l = w + 12. The height is the other side of the square at the end of the box. What is the relationsip between the width and the height? this will give youone equation with one unknown- no trial and error.
     
  14. Feb 20, 2007 #13
    humph....
    W H are the same therefore W subs H as W^2
    V=(W+12)W^2
    135=W^3 +12W^2
    0=W^3 +12W^2-135
    Cannot go any further therefore must use remainder theorem? Cannot use Quadratic theory, since its not a perfect parabola...
     
  15. Feb 20, 2007 #14
    Now that looks like the right equation! : )
    You have a cubic which in general has three roots.
     
  16. Feb 20, 2007 #15
    but how do i get 5 from that?
     
  17. Feb 20, 2007 #16
    To find the solution, now you can guess one of the roots by staring at the equation, then it will reduce to a simpler problem, essentially a quadratic (still a cubic though).
     
  18. Feb 20, 2007 #17
    In other words how do i solve for W?
     
  19. Feb 20, 2007 #18
    I dont think that 5 is a solution.
     
  20. Feb 20, 2007 #19
    Try a few small integers for w and see if any work.
     
  21. Feb 20, 2007 #20
    So... Make the question into an equation then break it down until it is simple to guess the variable?
     
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