SOLUTION: Hi there, I have a question where we are given the dimensions of a box : 18x20x6 , the box needs to have a larger volume of at least 5280. The question asks us to find the minimum

Question 831223: Hi there, I have a question where we are given the dimensions of a box : 18x20x6 , the box needs to have a larger volume of at least 5280. The question asks us to find the minimum dimensions of the box, but the length, width and height have to increase by the same amount.
By doing guess and check I figured out the dimensions of 22x24x10 which increases each by 4, but I am unsure of how to figure this out algebraically.
Thanks.
Answer by Elomeht(22) (Show Source): You can put this solution on YOUR website!
We set out to solve the problem by denoting the amount by which we increase each dimension as x. So sequentially:
1. (18 + x)(20 + x)(6 + x) = 5280
2. x^3 + 44x^2 + 588x - 3120 = 0
4. (x - 4)(x^2 + 48x + 780) = 0
5. x = 4 is clearly a solution; the other solutions are not real numbers
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