SOLUTION: A shipping container in a shape of a rectangular solid Nast have a volume of 351m³.The client tells the manufacturing that because of the contents, the length of the container mus
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-> SOLUTION: A shipping container in a shape of a rectangular solid Nast have a volume of 351m³.The client tells the manufacturing that because of the contents, the length of the container mus
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Question 1170782: A shipping container in a shape of a rectangular solid Nast have a volume of 351m³.The client tells the manufacturing that because of the contents, the length of the container must be 4m longer than the width, and the height must be 1/3 of the width. What should the dimensions of the container be? Answer by greenestamps(13203) (Show Source):
A solution using formal algebra, if one is required....
height = x
width = 3x [height is 1/3 of width]
length = 3x+4 [4 more than the width]
The volume is 351 (cubic meters):
To find the root(s) of that equation using formal algebra, you could use the rational roots theorem to find the possible rational roots and then use substitution or synthetic division to find one root; the roots of the remaining quadratic polynomial equation could be found by factoring or using the quadratic formula.
That's a lot of work -- but good exercise in those formal mathematical processes.
The solution(s) could be easily found using a graphing calculator.
But by far the easiest and fastest way to solve the problem is informally.
The prime factorization of 351 is
All we need to do to solve the problem is use those prime factors to get three numbers that satisfy the conditions of the problem.
It should be easy to see that works -- 3m is 1/3 of 9m; and 13m is 4m more than 9m.
