1.Elizabeth planned to make 6 pans of apple crisp for the day, using extra tart granny smith apples-just like her grandmother had. But after peeling, coring, and slicing she had a major problem: she only had 10 cups of apple slices. it was getting late and she needed to get some pans of apple crisp into the over. she knew that 10 cups of apple was 2 1/2 times as much 4 cups she needed, so she decided to use multiplication to figure 2 1/2 batches. Base on her hasty decision, how much each of each ingredient will she need?

2.After looking at her math, Elizabeth realized her mistake. She didn't have a pan that she could use for half a batch, and her math seemed too complicated anyway. she decided she would just make a double batch for now, because the she wouldn't need to multiply. using addition, how much of each ingredient would she need for a double batch?

3. The two pans of apple crisp were just starting to brown when Elizabeth returned from the store with more apples. But instead of tart apples, the store had only honeycrisp, a much sweeter variety. After preparing 14 more cups of apples, she could make 3 bathes using the honeycrisp (12 cups) and the fourth and final bath using both kinds of apples. Her concern, however was the sweetness of the apples. For the batches using the honeycrisp only, if the brown sugar and granulated sugar were reduced by 1/2 hot much sugar should she use for each batch? How much for all 3 batches?

1. To figure out how much of each ingredient Elizabeth will need for 2 1/2 batches of apple crisp, we need to find out the amount required for 1 batch and then multiply it by 2.5.

Since she initially needed 4 cups of apple slices for 1 batch, the amount needed for 2.5 batches would be:

4 cups/batch × 2.5 batches = 10 cups of apple slices

Therefore, Elizabeth will need 10 cups of apple slices for 2.5 batches of apple crisp.


2. Since Elizabeth decided to make a double batch instead, we need to determine the amounts of each ingredient required for a single batch and then double those amounts.

If she needed 4 cups of apple slices for 1 batch, for a double batch she would need:

4 cups/batch × 2 batches = 8 cups of apple slices

Therefore, Elizabeth will need 8 cups of apple slices for a double batch of apple crisp.

3. For the batches using the honeycrisp apples, if both types of sugar need to be reduced by 1/2, we can calculate the new amounts:

Let's assume that Elizabeth initially uses x cups of brown sugar and y cups of granulated sugar for each batch.

After reducing them by 1/2, the amounts of brown sugar and granulated sugar for each batch would be:

Brown sugar: x - (1/2)x = (1/2)x
Granulated sugar: y - (1/2)y = (1/2)y

Therefore, for each batch using honeycrisp apples, Elizabeth should use (1/2)x cups of brown sugar and (1/2)y cups of granulated sugar.

For all 3 batches, she would need a total of:

3 × (1/2)x cups of brown sugar and 3 × (1/2)y cups of granulated sugar.

1. To figure out how much of each ingredient Elizabeth will need, we need to calculate the ingredient quantities for 2 1/2 batches. Since Elizabeth needs 4 cups of apple slices for one batch, we can start by finding how many cups of apple slices she would need for 2 1/2 batches.

First, we need to find the total number of cups of apple slices for 2 batches. Since one batch requires 4 cups, two batches will require 4 cups/batch x 2 batches = 8 cups.

Next, we need to find the additional 1/2 batch. In this case, 1/2 batch would be half the amount needed for one full batch, which is 4 cups/2 = 2 cups.

So, for 2 1/2 batches, Elizabeth will need 8 cups for two batches plus an additional 2 cups for 1/2 batch, which totals to 8 cups + 2 cups = 10 cups of apple slices.

Now, we can calculate the quantities of other ingredients based on the apple slices needed. Since the question doesn't mention the specific amount of other ingredients for one batch, we can assume Elizabeth needs equal amounts of other ingredients as the apple slices.

Therefore, Elizabeth will need 10 cups of each ingredient for 2 1/2 batches.

2. Since Elizabeth decided to make a double batch, we can use addition instead of multiplication to determine the ingredient quantities.

If Elizabeth needs 4 cups of apple slices for one batch, for a double batch, she would need 4 cups/batch x 2 batches = 8 cups.

Therefore, Elizabeth will need 8 cups of each ingredient for a double batch.

3. For the batches using only honeycrisp apples, if Elizabeth wants to reduce both brown sugar and granulated sugar by 1/2, she should use half of the original quantities.

Let's assume the original quantities of brown sugar and granulated sugar for one batch are 'x' cups each.

To reduce them by 1/2, Elizabeth should use 1/2 * x cups for each of them in each batch using honeycrisp apples.

For all three batches that use honeycrisp apples, she should use 1/2 * x cups * 3 = 3/2 * x cups in total.

Note: The question doesn't specify the original quantity of sugar, so this is a generalized explanation.