Sure, let's solve this problem step by step.
1. Determine the total number of people:
- There are 35 students in the math club.
- Mrs. Penney also needs a muffin for herself.
Therefore, the total number of people is:
[tex]\[
35\, \text{students} + 1\, \text{teacher} = 36\, \text{people}
\][/tex]
2. Calculate the number of muffins needed:
- Since each person gets one muffin, we need 36 muffins in total.
3. Determine the number of muffins each batch makes:
- Each batch makes 12 muffins.
4. Calculate the number of batches needed:
- To find out how many batches are required to make at least 36 muffins, we divide the total number of muffins needed by the number of muffins per batch and round up to the nearest whole number since you can't make a fraction of a batch.
[tex]\[
\text{Number of batches} = \lceil \frac{36}{12} \rceil
\][/tex]
This simplifies to:
[tex]\[
\frac{36}{12} = 3
\][/tex]
Since 3 is already a whole number, we don’t need to round.
Therefore, Mrs. Penney needs 3 batches to make enough muffins for everyone.
Finally, let's summarize the solution in the provided table format.
\begin{tabular}{|l|l|l|l|l|}
\hline
\multicolumn{2}{|l|}{Blueberry Breakfast Treats} \\
\hline
Number of Batches & 1 & 2 & 3 & 4 \\
\hline
Cups of Blueberries & - & - & - & - \\
\hline
\end{tabular}
[tex]\[
\boxed{3}
\][/tex]
So, Mrs. Penney needs to prepare 3 batches of Blueberry Breakfast Treats.
