



 
Hi Tehmas, Suppose the height of the gift box is $x$ cm then, since the dimensions are consecutive positive integers, the width is $x + 1$ cm and the length is $x + 2$ cm. Thus the volume of the gift box is $x(x + 1)(x + 2) \mbox{ cm}^3.$ What are the dimensions of the larger box? What is the expression for its volume? The problem states that \[ \mbox{Volume of the larger box } = x(x + 1)(x + 2) + 456 \mbox{ cm}^3\] Solve for $x.$ When I did this the value of $x$ that I obtained was not an integer. Are you sure that you have the problem stated correctly? Harley  


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