Question

An engineer is designing a storage compartment in a space craft. The compartment must be 3

meters longer than it is wide, and its depth must be 1 meter less than its width. The volume of the
compartment must be 10 cubic meters. What is the width of the storage compartment?

Answer 1

9514 1404 393

Answer:

D. 2 m

Explanation:

You know the integer factors of 10 are 1, 2, 5, so a width of 2 m will satisfy the requirements. For a width of 2 m, the length is 2+3 = 5 m, and the depth is 2-1 = 1 m. The volume is ...

V = LWH = 5×2×1 = 10 . . . . cubic meters, as required

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If you were to write an equation for this, it would be a cubic. Let x = width, then length is x+3 and depth is x-1. The volume is ...

V = (x+3)(x)(x-1)

we want that equal to 10.

In standard form, the equation becomes ...

x^3 +2x^2 -3x -10 = 0

According to the Rational Root Theorem, positive rational roots will be from the set {1, 2, 5, 10}, which are the integer divisors of 10.

You can try these values, or you can use a graphing calculator to find the solution. I find a graphing calculator to be quick and easy.

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The width of the storage compartment is 2 meters.