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

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

1. The baker sold 40% of the tarts in the morning. So, after the morning sales, the number of tarts left is:
   \[
   \text{Tarts left after morning} = x - 0.4x = 0.6x
   \]

2. In the afternoon, the baker sold 40% of the remaining tarts. So, he sold 40% of \( 0.6x \), which is:
   \[
   \text{Tarts sold in the afternoon} = 0.4 \times 0.6x = 0.24x
   \]

3. After the afternoon sales, the number of tarts left is:
   \[
   \text{Tarts left after afternoon} = 0.6x - 0.24x = 0.36x
   \]

4. We are told that the baker had 54 tarts left at the end of the day. Therefore:
   \[
   0.36x = 54
   \]

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

Thus, the baker originally baked **150 tarts**.

Would you like further clarification on any of the steps? Here are some related questions:

1. How do you calculate percentages in general math problems?
2. What are the key differences between percentages and fractions?
3. How can you set up and solve other percentage-based word problems?
4. What would happen if the baker had sold 50% in the morning instead?
5. How does changing the percentage sold in the afternoon affect the final count of remaining tarts?

**Tip:** When solving percentage problems, it's often easier to express percentages as decimals to simplify calculations.

Discover how to solve a real-world math problem involving percentages and proportions. A baker sold 40% of his tarts in the morning, 40% of the remaining tarts in the afternoon, and was left with 54 tarts. Learn the step-by-step solution to find out how many tarts he baked initially. Suitable for Grades 6-8.

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