1. **State the problem:** Lin had 90 flyers. She gave 12 flyers to each of three volunteers, then divided the remaining flyers equally among the three volunteers. We need to identify which diagram represents this story. 2. **Analyze Diagram A:** It shows three parts labeled $x$ and one part labeled 12, totaling 90. This suggests $3x + 12 = 90$, which does not match the story because 12 flyers were given to each volunteer, not just once. 3. **Analyze Diagram B:** It shows three equal parts labeled $y + 12$ each, totaling 90. This matches the story: each volunteer got 12 flyers plus an equal share $y$ of the remaining flyers. So, $3(y + 12) = 90$. 4. **Conclusion:** Diagram B correctly represents the story. --- 5. **Solve the equation:** $6x + 11 = 21$ 6. **Step 1:** Subtract 11 from both sides: $$6x + \cancel{11} - \cancel{11} = 21 - 11$$ $$6x = 10$$ 7. **Step 2:** Divide both sides by 6: $$\frac{6x}{\cancel{6}} = \frac{10}{6}$$ $$x = \frac{10}{6} = \frac{5}{3}$$ 8. **Interpretation:** The value of $x$ is $\frac{5}{3}$, which satisfies the equation and matches the diagram where six parts labeled $x$ plus 11 equal 21. **Final answers:** - Diagram representing the flyer story: Diagram B - Solution to equation $6x + 11 = 21$: $x = \frac{5}{3}$