1. **State the problem:** We need to find which payment option is cheaper for a group of 10 students at an art gallery. 2. **Define the variables and expressions:** Let $n$ be the number of students. - Option 1: $8$ per student, so the total cost is $$8n$$. - Option 2: A $15$ group fee plus $2$ per student, so the total cost is $$15 + 2n$$. 3. **Substitute $n=10$ into each expression:** - Option 1 cost: $$8 \times 10 = 80$$ - Option 2 cost: $$15 + 2 \times 10 = 15 + 20 = 35$$ 4. **Compare the costs:** - Option 1 costs $80$. - Option 2 costs $35$. 5. **Conclusion:** Option 2 is cheaper for a group of 10 students. **Final algebraic expressions:** - Option 1: $$8n$$ - Option 2: $$15 + 2n$$