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**Question 3.1**:
A baker made some tarts. He sold \( 40\% \) of the tarts in the morning, \( \frac{3}{5} \) of the remaining tarts in the afternoon, and had 54 tarts left. How many tarts did he bake altogether?

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Let the total number of tarts the baker made be \( x \).

1. He sold \( 40\% \) of the tarts in the morning, so the number of tarts left after the morning sale is:
   \[
   \text{Remaining tarts} = x - 0.4x = 0.6x
   \]

2. In the afternoon, he sold \( \frac{3}{5} \) of the remaining tarts. Therefore, the number of tarts sold in the afternoon is:
   \[
   \text{Tarts sold in the afternoon} = \frac{3}{5} \times 0.6x = 0.36x
   \]
   The number of tarts left after the afternoon sale is:
   \[
   \text{Remaining tarts after afternoon sale} = 0.6x - 0.36x = 0.24x
   \]

3. According to the problem, 54 tarts were left after both sales. Therefore, we set up the equation:
   \[
   0.24x = 54
   \]

4. Solving for \( x \):
   \[
   x = \frac{54}{0.24} = 225
   \]

Therefore, the baker made **225** tarts altogether.

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Would you like more details or have any further questions?

Here are 5 related questions to deepen your understanding:

1. What fraction of the total tarts did the baker sell by the end of the day?
2. If the baker had sold \( 50\% \) of the tarts in the morning instead, how many tarts would he have left after both sales?
3. How would the final number of remaining tarts change if the baker sold \( \frac{4}{5} \) of the remaining tarts in the afternoon?
4. What percentage of the tarts did the baker sell in total?
5. How would you set up the equation if the problem stated the number of remaining tarts as a different value?

**Tip**: When solving percentage-based problems, converting percentages to decimals can simplify the equations and help you solve them more efficiently.

A baker made some tarts. He sold 40% of the tarts in the morning, 3/5 of the remaining tarts in the afternoon, and had 54 tarts left. How many tarts did he bake altogether?

Learn how to solve a percentage and fraction-based word problem about a baker who sells 40% of his tarts in the morning and 3/5 of the remaining tarts in the afternoon, leaving him with 54 tarts. A step-by-step algebraic solution is provided. Suitable for students in Grades 6-8.

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