Question

The dimensions of a rectangular bin are consecutive integers. If the volume of the bin is 4896 cubic inches, what are the dimensions of the bin? a. 12 x 18 x 24 c. 15 x 17 x 19 b. 16 x 17 x 18 d. 17 x 18 x 19

Answer 1

Let's use an equation to solve this problem.

Since they are consecutive integers, if we say that the first number is $x$, then the next two numbers (three dimensions in a rectangular prism) are $x+1$ and $x+2$ respectively.

$x*(x+1)*(x+2)=4896$

$x*(x+1)=x^2+x$

$(x^2+x)*(x+2)=x^3+2x^2+2x$

$x^3+3x^2+2x=4896$

$x^3+3x^2+2x-4896=0$

$x=16$

B is the correct answer.