Question

Compare the area of the bases. If a base has a greater area, it will take up more space on the shelf. Base area of Box 1: 3x2 Base area of Box 2: 4x2 – x Which box is likely to occupy more space on the shelf? Explain. Try substituting different values for x.

Answer 1

Base area of box 1: 3x2= 6 (this value  remains constant)

base area of box 2 if x=0
4x2-0= 8>6

base area of box 2 if x=1
4x2-1= 7>6

base area of box 2 if x=2
4x2-2= 6

base area of box 2 if x=3
4x2-3=5<6

base area of box 2 if x=4
4x2-4=4<6

base area of box 2 if x=5
4x2-5=3<6

base area of box 2 if x=6
4x2-6=2<6

base area of box 2 if x=7
4x2-7=1<6

box 2 is more likely to occupy more space on the shelf. It has a probability of 5/8 of occupying more space on the shelf.

Answer 2

If x = 1, the base areas are the same. But if x is greater than 1, then Box 2 has a greater base area. Therefore, Box 2 is likely to occupy more space on the shelf.