An eight-inch square cake serves six people.how many twelve-inch square cakes do you need to provide equivalent servings for eighteen people?
A = 8 * 8
A = 64 sq. inches
64/6 = 10.66667 sq. in. each
10.66667 * 18 = 192 square inches
12 in square cake = 144 sq. in
So how many cakes?
2 cakes
To determine how many twelve-inch square cakes are needed to provide equivalent servings for eighteen people, we need to adjust the portions based on the difference in cake sizes.
Step 1: Calculate the area of the eight-inch square cake:
An eight-inch square cake has a length and width of 8 inches each. So, the area can be calculated as:
Area = Length * Width = 8 inches * 8 inches = 64 square inches
Step 2: Calculate the servings per square inch:
Since the eight-inch square cake serves six people, we can calculate the servings per square inch by dividing the area of the cake by the number of servings:
Servings per square inch = 6 servings / 64 square inches ≈ 0.094 servings per square inch
Step 3: Calculate the required area for eighteen people:
To determine the required area to serve eighteen people, we need to multiply the desired number of servings by the servings per square inch:
Required area = 18 servings / 0.094 servings per square inch ≈ 191.49 square inches
Step 4: Calculate the number of twelve-inch square cakes needed:
Since the area of the twelve-inch square cake is 144 square inches (12 inches * 12 inches), we can calculate the number of cakes needed by dividing the required area by the area of each cake:
Number of cakes needed = Required area / Area of each cake = 191.49 square inches / 144 square inches ≈ 1.33 cakes
Therefore, you would need around 1.33 twelve-inch square cakes to provide equivalent servings for eighteen people. Since you can't have a fraction of a cake, you would need to round up to the next whole number. In this case, you would need at least 2 twelve-inch square cakes to ensure enough servings for eighteen people.