1. **State the problem:** A number $n$ when divided by 7 leaves a remainder of 3. We need to find the remainder when $4n + 5$ is divided by 7. 2. **Express the given condition mathematically:** Since $n$ leaves a remainder 3 when divided by 7, we can write: $$n = 7k + 3$$ where $k$ is an integer. 3. **Substitute $n$ into $4n + 5$:** $$4n + 5 = 4(7k + 3) + 5 = 28k + 12 + 5 = 28k + 17$$ 4. **Divide $4n + 5$ by 7 and find the remainder:** Since $28k$ is divisible by 7 (because $28k = 7 \times 4k$), it leaves no remainder. So the remainder depends on $17$ divided by 7. 5. **Calculate remainder of 17 divided by 7:** $$17 = 7 \times 2 + 3$$ So the remainder is 3. **Final answer:** The remainder when $4n + 5$ is divided by 7 is **3**.