1. **State the problem:** We need to find how many adults and children attended the movie given that 61 people attended in total and the total amount paid was 472. 2. **Define variables:** Let $a$ be the number of adults and $c$ be the number of children. 3. **Write the system of equations:** - Total people: $$a + c = 61$$ - Total cost: $$10a + 7c = 472$$ 4. **Solve the system:** From the first equation, express $c$ as $$c = 61 - a$$ 5. Substitute into the second equation: $$10a + 7(61 - a) = 472$$ 6. Simplify: $$10a + 427 - 7a = 472$$ $$3a + 427 = 472$$ 7. Subtract 427 from both sides: $$3a = 472 - 427$$ $$3a = 45$$ 8. Divide both sides by 3: $$a = \frac{\cancel{3}a}{\cancel{3}} = \frac{45}{3}$$ $$a = 15$$ 9. Find $c$: $$c = 61 - 15 = 46$$ 10. **Answer:** 15 adults and 46 children attended the movie.