Kate wanted to have a cake in which Elmos’ nose was 6 inches in diameter, because the preschool is 6 years old. Her original recipe of the cake batter called for: 3 eggs, 2 baking mix, Half a cup of oil, 1 cup of water. How much of each ingredient will she need? Explain how you know it.
9,6,1 1/2, 3
No way to tell. What size cake did those ingredients make?
To determine the amount of each ingredient Kate will need to make the desired cake with Elmo's nose being 6 inches in diameter, we first need to understand how the size of the cake relates to the quantities of the ingredients.
Given:
Original recipe:
- 3 eggs
- 2 baking mix
- Half a cup of oil
- 1 cup of water
Desired cake:
- Elmo's nose (target diameter) = 6 inches
Since the recipe for the original cake does not inherently mention anything specific about the size of the cake, we can assume that it yields a standard-sized cake. Therefore, we need to scale up the recipe to match the desired size.
Given that the only aspect that changes within the desired cake is the diameter of Elmo's nose, we can conclude that the other dimensions of the cake (height, length, etc.) remain the same.
To maintain the same dimensions of the original recipe except for the diameter, we can use the concept of ratios. By comparing the changes in the diameter, we can determine how the quantities of the ingredients should be adjusted.
Let's assume that Kate's desired cake will have a diameter of 6 inches (which corresponds to Elmo's nose). Additionally, let's assume the original recipe yields a cake with a diameter of 3 inches.
To determine the scaling factor, divide the desired diameter by the original diameter:
Scaling factor = desired diameter / original diameter = 6 inches / 3 inches = 2
Now we can use this scaling factor to adjust the quantities of the ingredients:
- Eggs: Multiply the original quantity by the scaling factor:
3 eggs * 2 (scaling factor) = 6 eggs
- Baking mix: Multiply the original quantity by the scaling factor:
2 baking mix * 2 (scaling factor) = 4 baking mix
- Oil: Multiply the original quantity by the scaling factor:
0.5 cups of oil * 2 (scaling factor) = 1 cup of oil
- Water: Multiply the original quantity by the scaling factor:
1 cup of water * 2 (scaling factor) = 2 cups of water
Therefore, Kate will need:
- 6 eggs
- 4 baking mixes
- 1 cup of oil
- 2 cups of water
This adjustment in the quantities ensures that she will have enough ingredients to make a cake with a 6-inch diameter for Elmo's nose.
Remember that these measurements are based on the assumption that the size of Elmo's nose is directly proportional to the diameter of the cake. Adjustments may need to be made if additional modifications to the cake's dimensions are desired.