Alright, let's break down the problem step-by-step to determine how many batches Mrs. Penney needs to make and how many cups of blueberries she will require.
1. Determine the Total Number of Muffins Needed:
Mrs. Penney wants to make sure that each of the 35 students and herself (35 + 1 = 36 people) get one muffin. So, the total number of muffins needed is 36.
2. Calculate the Number of Batches Required:
Each batch makes 12 muffins. Therefore, we need to find out how many batches are necessary to have at least 36 muffins. Since a batch cannot be divided and has to be a whole number, here’s how we calculate it:
[tex]\[
\text{Number of Batches} = \left\lceil \frac{36}{12} \right\lceil
\][/tex]
We get 3 batches (since [tex]\(36 \div 12 = 3\)[/tex], we don't even need to round up anything).
3. Determine Cups of Blueberries Needed Per Batch:
According to the problem, each batch requires [tex]\(\frac{2}{4}\)[/tex] or 0.5 cups of blueberries.
4. Calculate the Total Cups of Blueberries Required:
Since we need 3 batches, we multiply the number of batches by the cups of blueberries needed per batch:
[tex]\[
\text{Total Cups of Blueberries} = 3 \times 0.5 = 1.5 \text{ cups}
\][/tex]
In summary:
- The total number of people is 36.
- The number of batches required is 3.
- The total cups of blueberries needed is 1.5 cups.
Thus, according to your question and given values, Mrs. Penney needs to make 3 batches to have at least 36 muffins, and she will need a total of 1.5 cups of blueberries to do so.
