How do you solve?

Question

 Paula’s Paper Packaging is mailing boxes of notebook paper to an office supply store. The dimensions of each stack of notebook paper are 11 inches by 8.5 inches by 3 inches.  

1. Paula is putting 12 stacks of paper in each box. If she has a choice of the three boxes below, which one should she choose? Show how you found your answer. 

Box 1: 30 inches by 35 inches by 32 inches

Box 2: 30 inches x 34 inches x 65 inches

Box 3: 25 inches x 35 inches x 50 inches

Answer 1

Hello! We are given the length, width and height of one stack of paper. We know the volume (V) of this stack (in the shape of a rectangular prism) can be found using the formula: V = lwh = (11 in.)(8.5 in)(3 in).

This gives us a volume of 280.5 in³.

Next we have to find the volume of our stack(s)! Not just once, but 12 times (hence the 12 stacks).

12 x 280.5 = 3, 366 in³ (12 stacks of our paper).

CRUCIAL - Now lets see which one fits the BEST! To do this, we first find the volume of each box (using our formula V=lwh)...

Box 1 = 33, 600

Box 2 = 66, 300

Box 3 = 43, 750

NEXT - Our volume of our paper has to be able to fit into one of these boxes, so we've gotta divide! (Just like in order for 3 to "fit" into 12, we must have 12 ÷ 3).

 To do this, we must have: Box VOLUME ÷ Paper Volume. Let's calculate this for all three boxes with the volume we found from 12 stacks of paper. (I will round to the nearest tenth).

Box 1 / 12 stacks of Paper Volume = 9.9

Box 2 / 12 stacks of Paper Volume = 19.7

Box 3 / 12 stacks of Paper Volume = 12.9

Box 1 is less than 12, so it can't even fit 12! Box 2 has enough but much more volume than we need.

Box 3 is the correct answer. Always choose the box that not only has enough, but is closest to the amount of items you need!