- Identify the total number of muffins as \(M\).
- Create the equation \(0.12 \times M = 30\) representing the given percentage relationship.
- Solve for \(M\) by calculating \(\frac{30}{0.12}\).
- The final result is \(\boxed{250}\).
Explanation
- Defining the Problem and Establishing the Equation
To determine the total number of muffins Jane made, let \(M\) represent the total quantity. We are given that Jane brought 30 muffins to work, which corresponds to exactly 12% of the total number of muffins she made. This relationship can be expressed by the following linear equation:
\[0.12 \times M = 30\]
Our goal is to solve for \(M\) to find the total number of muffins.
- Solving for the Total Number of Muffins
To find \(M\), we need to isolate the variable on one side of the equation. We do this by dividing both sides by 0.12:
\[M = \frac{30}{0.12}\]
To simplify this division, we can multiply both the numerator and the denominator by 100:
\[M = \frac{3000}{12}\]
Now, performing the division, we find:
\[M = 250\]
Therefore, the total number of muffins Jane made is 250.
Examples
Understanding how to calculate totals from percentages is incredibly useful in everyday life, such as when determining the original price of an item during a sale. For example, if a store displays that a 20% discount on an item is \$10, you can calculate the original price \(P\) by setting up the equation \(0.20 \times P = 10\), which reveals that the item originally cost \(\$50\). Mastering these proportions allows you to manage budgets, analyze trends, and understand data effectively.