Let's break down the problem step by step to understand how many batches of muffins are needed and the corresponding amount of blueberries required.
1. Total people to receive muffins:
- Mrs. Penney has 35 students and herself, making it a total of [tex]\( 35 + 1 = 36 \)[/tex] people who need muffins.
2. Muffins per batch:
- Each batch of muffins makes 12 muffins.
3. Number of batches required:
- To find out how many batches are needed, we need to divide the total number of people (36) by the number of muffins each batch makes (12). The calculation is [tex]\( \frac{36}{12} = 3 \)[/tex].
Hence, Mrs. Penney needs 3 batches of muffins to ensure each of the 36 people gets one muffin.
4. Cups of blueberries per batch:
- According to the table, each batch of muffins requires [tex]\( \frac{1}{4} \)[/tex] cup of blueberries.
5. Total cups of blueberries needed:
- If each batch needs [tex]\( \frac{1}{4} \)[/tex] cup of blueberries and she is making 3 batches, the total amount of blueberries needed is [tex]\( 3 \times \frac{1}{4} = \frac{3}{4} \)[/tex] cup = 0.75 cups.
Therefore, the detailed solution is as follows:
- Mrs. Penney needs to prepare 3 batches of muffins.
- To make these 3 batches, she will need 0.75 cups of blueberries.
