Subjects algebra

House Profit Loss 36A681

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1. **State the problem:** Ms. A owns a house worth 10000. She sells it to Mr. B at a 10% profit, then Mr. B sells it back to Ms. A at a 10% loss. We need to find how much money Ms. A makes. 2. **Calculate the selling price from Ms. A to Mr. B:** Ms. A sells at 10% profit, so selling price = cost price + 10% of cost price $$\text{Selling price} = 10000 + 0.10 \times 10000 = 10000 + 1000 = 11000$$ 3. **Calculate the selling price from Mr. B back to Ms. A:** Mr. B sells at 10% loss on his cost price (which is 11000), so selling price = cost price - 10% of cost price $$\text{Selling price} = 11000 - 0.10 \times 11000 = 11000 - 1100 = 9900$$ 4. **Calculate Ms. A's net money after both transactions:** Ms. A initially had the house worth 10000. She sold it for 11000, so she gained 1000. Then she bought it back for 9900, so she spent 9900. Her net money = amount received from first sale - amount paid in second purchase $$\text{Net money} = 11000 - 9900 = 1100$$ 5. **Interpretation:** Ms. A makes a net profit of 1100 after both transactions. **Final answer:** Ms. A makes 1100 money units.