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Exercises Equations and inequalities

Example 6 from Algebra and Trigonometry, 2.3 Models and Applications

Solving a Volume Problem

Find the dimensions of a shipping box given that the length is twice the width, the height is $8$ inches, and the volume is 1,600 in.³.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The formula for the volume of a box is given as $V = L W H,$ the product of length, width, and height. We are given that $L = 2 W,$ and $H = 8.$ The volume is $1,600$ cubic inches.

$\begin{matrix} V & = & L W H \\ 1, 600 & = & (2 W) W (8) \\ 1, 600 & = & 16 W^{2} \\ 100 & = & W^{2} \\ 10 & = & W \end{matrix}$
The dimensions are $L = 20$ in., $W = 10$ in., and $H = 8$ in.

How did it go?

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From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 2.3, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.