Question: A bakery sold $138$ mocha cupcakes in a day, which was $46\%$ of the total number of cupcakes sold that day. How many total cupcakes did the bakery sell that day?
1. **State the problem:** We know the bakery sold $138$ mocha cupcakes, which is $46\%$ of the total cupcakes sold. We need to find the total number of cupcakes sold that day.
2. **Formula:** If $x$ is the total number of cupcakes sold, then $46\%$ of $x$ equals $138$. Mathematically, this is:
$$0.46 \times x = 138$$
3. **Solve for $x$:**
$$x = \frac{138}{0.46}$$
4. **Simplify the fraction:**
$$x = \frac{\cancel{138}}{\cancel{0.46}}$$
(Here, we show the cancellation conceptually, but since these are decimal and integer, we proceed to division.)
5. **Calculate:**
$$x = 300$$
6. **Interpretation:** The bakery sold a total of $300$ cupcakes that day.
**Final answer:** $300$ cupcakes.