Jan is making a 3-tier wedding cake for 300 guests. She will make the cake for $3 per serving with the following specifications:
-Each serving is 4 inch.3
-Each tier must be smaller than the tier below it.
-Each square tier is 4 in. tall with a side length of 16 in., 14 in., 12 in., 10 in., 8 in., or 6.in
What is the cost of the most economical 3-tier cake that will serve 300 people?
so, we need to divide each tier into 1" square pieces.
we need a^2+b^2+c^2 >= 300
6^2 = 36
8^2 = 64
10^2 = 100
12^2 = 144
14^2 = 196
16^2 = 256
a b c sum
6 8 10 200
6 8 12 244
6 8 14 296
6 8 16 356
8 10 12 308
That's it. Any other combination will be way over 308 servings.
Not sure why $3/serving was specified, since the cost makes no difference in the choice. Now, if different size layers had different cost per serving, that would change things.
To determine the cost of the most economical 3-tier cake that will serve 300 people, we need to consider the number of servings provided by each tier and the cost per serving. Here's how we can calculate it:
Step 1: Calculate the number of servings provided by each tier.
- Start by calculating the number of servings for each tier using the given dimensions.
- We know that each serving is 4 in. x 4 in. x 3 in., which gives a volume of 48 cubic inches.
- Find the volume of each tier by multiplying the base area (side length squared) by the height.
- The tiers available are 16 in., 14 in., 12 in., 10 in., 8 in., and 6 in.
For the first tier (the bottom one):
- Base area = 16 in. x 16 in. = 256 square inches
- Volume = 256 sq. in. x 4 in. = 1024 cubic inches
- Number of servings = Volume / 48 cubic inches
For the second tier:
- Base area = 14 in. x 14 in. = 196 square inches
- Volume = 196 sq. in. x 4 in. = 784 cubic inches
- Number of servings = Volume / 48 cubic inches
For the third tier (the top one):
- Base area = 12 in. x 12 in. = 144 square inches
- Volume = 144 sq. in. x 4 in. = 576 cubic inches
- Number of servings = Volume / 48 cubic inches
Step 2: Calculate the total number of servings provided by the 3-tier cake.
- Add up the number of servings from each tier.
- Total servings = number of servings from the bottom tier + number of servings from the second tier + number of servings from the top tier
Step 3: Calculate the cost of the most economical 3-tier cake.
- Multiply the total number of servings by the cost per serving ($3).
By following these steps, you can calculate the cost of the most economical 3-tier cake that will serve 300 people.