Question

A shipping company needs to determine the number of Styrofoam packing peanuts that fit per square foot in a box that measures 20 ft2
Question:

1. If 1300 packing peanuts fit in the box, how many packing peanuts are there per square foot in the box?

2. How many packing peanuts fit in a box that is 25% larger in volume?

3. Does the number of packing peanuts per square foot change for the larger box, and why?

Answer 1

1) We have 1300 packing peanuts, and 20 ft^2. Therefore, to find out how many packing peanuts there are per square foot, we divide the number of peanuts (1300) by the number of square feet (20 ft^2). This gives us 1300 / 20 = 65 packing peanuts per square foot.
2) We do not know the current volume of the box which fits the 1300 packing peanuts (all we know is its area). But it is reasonable to expect that if we increase the volume by 25%, the number of packing peanuts will also increase by 25%. This means we can fit 1300*(1.25) = 1625 peanuts in the larger box.
3) This will depend on how the box is larger. If its height remains the same, and its floor area increases to accommodate the greater volume, then the number of packing peanuts per square foot remains the same.
However, if the height of the box is different, then the number of packing peanuts per square foot will change, since the floor area will not increase by the same 25% any more.