1. **State the problem:** Riley bought bags of popcorn and drinks totaling 51 dollars. Each bag of popcorn costs 5 dollars, each drink costs 6 dollars, and she bought twice as many drinks as bags of popcorn. 2. **Define variables:** Let $x$ be the number of bags of popcorn and $y$ be the number of drinks. 3. **Write the system of equations:** - Total cost: $$5x + 6y = 51$$ - Relationship between quantities: $$y = 2x$$ 4. **Substitute $y$ in the first equation:** $$5x + 6(2x) = 51$$ $$5x + 12x = 51$$ $$17x = 51$$ 5. **Solve for $x$:** $$x = \frac{51}{17}$$ $$x = 3$$ 6. **Find $y$ using $y = 2x$:** $$y = 2 \times 3 = 6$$ 7. **Answer:** Riley bought **3** bags of popcorn and **6** drinks.