Question

The volume of the cereal box must be 192in 3 . A box of cereal has a height of (x+10) inches, a width of (x−4) inches, and a length of x inches. In the context of this problem, which solutions to the polynomial equation can you eliminate because they do not make sense?

a.x=−8
b. x=−4
c. x=6

Answer 1

Options a and b are eliminated because negative dimensions for a box do not make sense. Option c, x=6, is the only possible solution that gives the box a positive volume, matching the required 192 cubic inches.

Step-by-step explanation:

The student has presented a problem regarding the volume of a cereal box with the dimensions expressed in terms of the variable x. The volume of the box is given as 192 cubic inches, and the dimensions are height (x+10) inches, width (x−4) inches, and length x inches. The equation representing the volume is thus x(x+10)(x−4) = 192.

Looking at the potential solutions a. x=−8, b. x=−4, and c. x=6, we can eliminate options a and b because a box cannot have negative dimensions. Therefore, the only possible physical solution from the given options is x=6 inches. Substituting x into the equation with x=6 yields a volume that matches the required 192 cubic inches (since 6*(6+10)*(6−4) = 192), confirming that this is the correct solution.