3. Gregory borrowed money to buy a used car, which he paid back at the end of the loan period. It cost him \( \$ 10,650 \) to repay the loan. How many years was the loan period? A. How much did Gregory pay in interest? \( \$ \$ 3,150 \) \( \$ 18,650 \)

To solve the problem, we need to extract the known conditions and then calculate the interest paid by Gregory. 1. **Known Conditions:** - Total amount repaid: \( \$ 10,650 \) - We need to find out how much Gregory paid in interest and the duration of the loan period. 2. **Calculating Interest:** - The problem does not provide the principal amount (the original loan amount) or the interest rate. However, we can infer that the total repayment amount includes both the principal and the interest. - Let's denote: - \( P \) = Principal amount (the amount borrowed) - \( I \) = Interest paid - Total repayment = \( P + I \) Given that the total repayment is \( \$ 10,650 \), we can express the interest as: \[ I = 10,650 - P \] The options provided for the interest are \( \$ 3,150 \) and \( \$ 18,650 \). - If we assume \( I = 3,150 \): \[ P = 10,650 - 3,150 = 7,500 \] - If we assume \( I = 18,650 \): \[ P = 10,650 - 18,650 = -8,000 \quad (\text{not possible since } P \text{ cannot be negative}) \] Therefore, the only feasible option is \( I = 3,150 \). 3. **Conclusion:** - Gregory paid \( \$ 3,150 \) in interest. - The principal amount borrowed was \( \$ 7,500 \). 4. **Loan Period:** - The problem does not provide enough information to determine the loan period directly. We would need either the interest rate or additional details about the loan terms to calculate the duration. Thus, the answer to part A is: - Gregory paid \( \$ 3,150 \) in interest. For the loan period, we need more information to provide an answer.