1. **State the problem:** Amelia invested 600 in an account with 10% simple interest per year. We want to find how many years, $t$, it will take for the investment to be worth 3000. 2. **Formula used:** The simple interest formula is $$A = P + Prt$$ where: - $A$ is the amount after $t$ years - $P$ is the principal (initial amount) - $r$ is the interest rate as a decimal - $t$ is the time in years 3. **Substitute known values:** $$3000 = 600 + 600 \times 0.10 \times t$$ 4. **Simplify the equation:** $$3000 = 600 + 60t$$ 5. **Isolate $t$:** $$3000 - 600 = 60t$$ $$2400 = 60t$$ 6. **Divide both sides by 60:** $$t = \frac{2400}{60}$$ 7. **Cancel common factors:** $$t = \frac{\cancel{2400}^{40}}{\cancel{60}^{1}} = 40$$ 8. **Answer:** It will take 40 years for the investment to be worth 3000. **Final answer:** 40