A sold a table to B at a profit of 15% Later on, B sold it back to A at a profit of 20%, thereby gaining $69. How much did A pay for the table anginally?

Let's solve the problem step by step.

### Step 1: Define Variables
- Let the original price at which A bought the table be $ x $.
- A sold the table to B at a 15% profit, so B bought the table for:
  \[
  \text{Price B bought it from A} = x + 0.15x = 1.15x
  \]
- B then sold the table back to A at a 20% profit. The price at which B sold the table to A is:
  \[
  \text{Price B sold it to A} = 1.15x + 0.2(1.15x) = 1.15x(1 + 0.2) = 1.15x \times 1.2 = 1.38x
  \]
- According to the problem, B gained $69 by selling the table back to A, so:
  \[
  \text{Gain} = \text{Selling Price} - \text{Cost Price} = 1.38x - 1.15x = 0.23x
  \]
  And we know that:
  \[
  0.23x = 69
  \]

### Step 2: Solve for $ x $
\[
x = \frac{69}{0.23} = 300
\]

### Final Answer:
A originally paid **$300** for the table.

Would you like more details, or do you have any further questions?

Here are some related questions:
1. What would be B's gain if the table was originally sold to B at a 20% profit instead of 15%?
2. How much would A pay to B if the profit percentage on B's resale was 25%?
3. If B sold the table to C at a 10% profit, how much did C pay?
4. What would be the gain if A bought the table for $250 originally?
5. How would the calculations change if the profit percentages were in reverse order?
6. What if A had initially sold the table at a loss of 10%?
7. How much would A gain or lose if A sold it back to B at the original price?
8. What is the percentage gain for A after the entire transaction?

**Tip:** When dealing with profit and loss problems, it's helpful to clearly define the cost price, selling price, and the profit or loss percentages to set up the correct equations.

Learn how to calculate the original price of an item based on profit and loss transactions. Solve a problem where A sells a table to B at a 15% profit, and B later sells it back to A at a 20% profit, gaining $69. Understand the step-by-step solution involving profit percentages and gain calculations. Suitable for high school students studying profit and loss problems.

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