Question

Suppose you work for a sporting goods company, and you want to order shipping boxes for bike helmets. Each helmet is already packaged in a smaller box that is n inches wide, n inches long, and 8 inches tall. The shipping boxes you order should accommodate the boxed helmet along with some packing material that will take up an extra 2 inches of space along the width and 4 inches of space along the length. The height of the shipping box should be the same as the helmet box. The volume of the shipping box needs to be 1,144 cubic inches. Which equation models the volume of the shipping box?

Answer 1

Answer:  $n^2+6n-135=0$

Step-by-step explanation:

The length, width and height of the smaller box are n inches , n inches and 8 inches respectively,

And, According to the question,

The shipping boxes has 2 inches extra width than that of smaller box and 4 inches extra length than that of smaller box, Also, The height of the shipping box should be the same as the helmet box.

Thus, the Length of the shipping box = (n + 4) inches

Width = (n+2) inches and height = 8 inches

Thus, the volume of the shipping box,

$V = (n+4)\times (n+2)\times 8=(n^2+6n+8)8=8n^2+48n+64$

But, V = 1,144 cubic inches,

⇒ $8n^2+48n+64=1144$

⇒ $n^2+6n+8=143$

⇒  $n^2+6n-135=0$

Which is the required equation that models the volume of the shipping box.