Question

Stephanie is making a three-tier wedding cake where the tiers are stacked from largest to smallest from bottom to top. The expression below represents the total circumference of all three tiers, where b is the circumference of the bottom tier.

1/4b+1/2b+b

Which statement best describes 1/2b?

A.The circumference of the top tier is half the circumference of the bottom tier.
B.The circumference of the middle tier is half the circumference of the bottom tier.
C.The circumference of the middle tier is half the circumference of the top tier.
D.The circumference of the top tier is half the circumference of the middle tier.

Answer 1

B. The circumference of the middle tier is half the circumference of the bottom tier

Explanation:

The problem statement tells you b represents the circumference of the bottom tier. The other tiers have circumferences of 1/2b and 1/4b. 1/4b is smaller than 1/2b, so must be the circumference of the top tier. Then 1/2b is the circumference of the middle tier, and it is half that of the bottom tier.

The circumference of the middle tier is half that of the bottom tier.

_____

It is also true that the circumference of the top tier (1/4b) is half that of the middle tier (1/2b). However, we're to comment on the meaning of 1/2b, not the meaning of 1/4b.

Answer 2

Answer: B. The circumference of the middle tier is half the circumference of the bottom tier.

Explanation:

Given : Stephanie is making a three-tier wedding cake where the tiers are stacked from largest to smallest from bottom to top.

Top

Structure of cake → Middle

Bottom

In Descending order of circumference: Bottom→ Middle→ Top (1)

Since , circumference of Bottom = b

The expression represents the total circumference of all three tiers =
`(1)/(4)b+(1)/(2)b+b`

In Descending order →
`b\to(1)/(2)b\to (1)/(4)b` (2)

From (1) and (2)

circumference of middle =
`(1)/(2)b` = half of b

circumference of top =
`(1)/(4)b` = One fourth of b

Hence, the statement best describes
`(1)/(2)b` is "The circumference of the middle tier is half the circumference of the bottom tier.".

Hence, the correct answer is Option (B)