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.

Who puts Preschool stuff on here? If you are smart enough to type this whole thing, then you can figure it out yourself! This is Preschool you lazy bum!

1. 9 eggs, 6 baking mix, 1-1/2 cups of oil, 3 cups of water. You are just tripling the ingredients.

2.10.50
4.3cups of red, 1-1/2 cps of black, 3/4cp of white and orange.
5.30inch platter

kma is corret

1. To determine how much of each ingredient she will need, we can use the concept of ratios. Since the requested Elmo's nose is 6 inches in diameter, which is three times the original 2-inch diameter, we can scale up the recipe proportionally.

The original recipe calls for:
- 3 eggs
- 2 baking mix
- 0.5 cups of oil
- 1 cup of water

To scale up the recipe, we multiply each ingredient by 3:
- 3 x 3 = 9 eggs
- 2 x 3 = 6 baking mix
- 0.5 x 3 = 1.5 cups of oil
- 1 x 3 = 3 cups of water

Therefore, to make the bigger cake, she will need 9 eggs, 6 baking mix, 1.5 cups of oil, and 3 cups of water.

2. If Kate spent $3.50 on the ingredients for the original cake, and she needs to scale up the recipe by three times, the director should give her three times the amount Kate spent.

$3.50 x 3 = $10.50

So the director should give Kate $10.50 for the ingredients.

3. Kate used 2 cups of frosting, with 1 cup of red, half a cup of black, and a quarter cup each of white and orange.

To determine how much of each frosting she needs for the bigger cake, we can scale up the proportions. Since the recipe is being scaled up by three times, we multiply each amount by 3.

- 1 cup x 3 = 3 cups of red frosting
- 0.5 cups x 3 = 1.5 cups of black frosting
- 0.25 cups x 3 = 0.75 cups each of white and orange frosting

Therefore, she will need 3 cups of red frosting, 1.5 cups of black frosting, and 0.75 cups each of white and orange frosting for the bigger cake.

4. Since the bigger cake doesn't have proportionally thicker frosting, we can use the same amount of frosting as the original cake.

So she will still need 1 cup of red frosting, 0.5 cups of black frosting, and 0.25 cups each of white and orange frosting.

5. Kate's first cake is on a 10-inch platter. To determine how big of a platter the director will need, we need to consider the proportional increase in size.

If Elmo's nose has increased from a 2-inch diameter to a 6-inch diameter (three times larger), the cake will also need to increase by the same proportion.

Since the original cake is on a 10-inch platter, the director will need a platter that is three times the size of 10 inches.

10 inches x 3 = 30 inches

Therefore, the director will need a 30-inch platter for the cake.