1. **State the problem:** Lina bought a smart TV with a down payment of 300 and 12 monthly payments of 245. The dealer charges 7% per annum simple interest on the original balance. We need to find the cash price of the TV. 2. **Define variables:** Let the cash price be $P$. 3. **Calculate total amount paid:** Total paid = down payment + 12 monthly payments = $300 + 12 \times 245 = 300 + 2940 = 3240$. 4. **Simple interest formula:** $$I = P \times r \times t$$ where $I$ is interest, $r$ is annual interest rate, and $t$ is time in years. 5. **Time period:** 12 months = 1 year, so $t = 1$. 6. **Original balance:** The original balance is the cash price minus the down payment, so $P - 300$. 7. **Total amount paid includes principal and interest:** $$\text{Total paid} = \text{Original balance} + I + \text{Down payment}$$ 8. Substitute $I$ and original balance: $$3240 = (P - 300) + (P - 300) \times 0.07 \times 1 + 300$$ 9. Simplify: $$3240 = (P - 300)(1 + 0.07) + 300 = (P - 300) \times 1.07 + 300$$ 10. Subtract 300 from both sides: $$3240 - 300 = (P - 300) \times 1.07$$ $$2940 = (P - 300) \times 1.07$$ 11. Divide both sides by 1.07: $$\frac{2940}{\cancel{1.07}} = (P - 300) \times \cancel{1.07}$$ $$2747.66 \approx P - 300$$ 12. Add 300 to both sides: $$P = 2747.66 + 300 = 3047.66$$ **Final answer:** The cash price of the TV is approximately 3047.66.