Kate made a birthday cake for Bryan’s second birthday. One of the guests on the party (who is a preschool director) thought how awesome it would be to have a cake like this for the Open House next week! She asked Kate to make one for her.
She wanted to have a cake in which Elmos’ nose was 6 inches in diameter, because the preschool is 6 years old. Elmo's nose is 2 inches in diameter now. The new cake will be proportionally taller as well. Her original recipe of the cake batter called for: 3 eggs, 2 baking mix, Half a cup of oil, 1 cup of water.
1. How much of each ingredient will she need? Explain how you know it.
2. If Kate spent $3.50 on the ingredients of the cake, how much money should the director give her for the ingredients?
3. Kate used altogether 2 cups of frosting: 1 cup of red, a half a cup of black, and a quarter cup of each white and orange.
4. How much of each frosting will she need for the big cake? Explain how you know it. (Keep in mind that the bigger cake doesn’t have proportionally thicker frosting…)
5. Kate’s first cake is on a 10-inch platter. How big of a platter will the director need for her cake? Explain how you know it.
Don't know the answers
1. To calculate how much of each ingredient the director will need for the bigger cake, we need to find the ratio of the sizes of Elmo's nose in the original cake and the new cake.
The original ratio can be calculated as 6 inches (new size) / 2 inches (original size) = 3.
By applying this ratio to the rest of the ingredients, we can determine the quantities needed for the new cake.
- Eggs: Multiply the original quantity (3 eggs) by the ratio (3), so the director will need 9 eggs.
- Baking mix: Multiply the original quantity (2 baking mix) by the ratio (3), so the director will need 6 baking mix.
- Oil: Multiply the original quantity (0.5 cup of oil) by the ratio (3), so the director will need 1.5 cups of oil.
- Water: Multiply the original quantity (1 cup of water) by the ratio (3), so the director will need 3 cups of water.
2. If Kate spent $3.50 on the ingredients of the cake, we don't have enough information to determine how much money the director should give her for the ingredients. The cost of the ingredients will depend on factors such as the price of each ingredient and any additional costs associated with making the cake.
3. For the original cake, Kate used 2 cups of frosting: 1 cup of red, a half a cup of black, and a quarter cup of each white and orange.
4. To determine how much of each frosting the director will need for the big cake, we can use the same ratio we used in question 1 to calculate the new quantities. Since the bigger cake doesn't have proportionally thicker frosting, we can maintain the same ratio for the frostings as well.
- Red frosting: Multiply the original quantity (1 cup of red frosting) by the ratio (3), so the director will need 3 cups of red frosting.
- Black frosting: Multiply the original quantity (0.5 cup of black frosting) by the ratio (3), so the director will need 1.5 cups of black frosting.
- White frosting: Multiply the original quantity (0.25 cup of white frosting) by the ratio (3), so the director will need 0.75 cups of white frosting.
- Orange frosting: Multiply the original quantity (0.25 cup of orange frosting) by the ratio (3), so the director will need 0.75 cups of orange frosting.
5. To determine how big of a platter the director will need for her cake, we can use the same ratio we used earlier to calculate the new diameter. Since the director wants Elmo's nose to be 6 inches in diameter, and the original nose is 2 inches in diameter, we have a ratio of 6 inches (new size) / 2 inches (original size) = 3.
For the platter, we need to calculate the new diameter by multiplying the original diameter (10 inches) by the ratio (3). Therefore, the director will need a platter with a diameter of 30 inches for her cake.