A baker made some lemon tarts. He sold 40% of the tarts in the morning, 2
5
of the 
remaining tarts in the afternoon and had 54 tarts left. How many tarts did he bake 
altogether?

Let's solve the problem step by step.

1. **Let the total number of tarts be** \( x \).

2. **He sold 40% of the tarts in the morning**, so the number of tarts sold in the morning is:
   \[
   0.4x
   \]
   Therefore, the number of tarts remaining after the morning sale is:
   \[
   x - 0.4x = 0.6x
   \]

3. **In the afternoon, he sold \(\frac{2}{5}\) of the remaining tarts**. The number of tarts sold in the afternoon is:
   \[
   \frac{2}{5} \times 0.6x = \frac{1.2x}{5} = 0.24x
   \]
   The number of tarts remaining after the afternoon sale is:
   \[
   0.6x - 0.24x = 0.36x
   \]

4. **We know that after selling in the afternoon, he had 54 tarts left**. Therefore:
   \[
   0.36x = 54
   \]

5. **Solve for \( x \)**:
   \[
   x = \frac{54}{0.36} = 150
   \]

So, the baker originally baked **150 tarts** altogether.

Would you like more details or have any questions about this problem? 

Here are some related questions you might find interesting:

1. If he sold 60% of the remaining tarts after the afternoon, how many would be left?
2. What fraction of the total tarts were sold in the afternoon?
3. If he had 200 tarts initially, how many would be left after selling 40% in the morning?
4. How many tarts did he sell in the morning and afternoon combined?
5. If the baker decided to sell an additional 30 tarts in the evening, how many would he have left?

**Tip:** When solving percentage-based problems, it's helpful to translate percentages into fractions or decimals to simplify calculations.

Learn how to solve a percentage problem involving lemon tarts. Follow a step-by-step solution to determine how many tarts the baker originally baked. Suitable for Grades 7-9 students learning about percentages and problem-solving.

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