1. **Problem Statement:** Melody wants to mix bags of M&M’s costing $4.89 each and Reese’s Pieces costing $3.79 each to make 25 bags total, with an average cost of $4.23 per bag. 2. **Define variables:** Let $x$ = number of M&M’s bags, $y$ = number of Reese’s Pieces bags. 3. **Formulate equations:** - Total bags: $$x + y = 25$$ - Total cost: $$4.89x + 3.79y = 4.23 \times 25$$ 4. **Simplify total cost equation:** $$4.89x + 3.79y = 105.75$$ 5. **Solve system by substitution:** From first equation, $$y = 25 - x$$ 6. Substitute into cost equation: $$4.89x + 3.79(25 - x) = 105.75$$ $$4.89x + 94.75 - 3.79x = 105.75$$ $$\cancel{4.89x} - \cancel{3.79x} + 94.75 = 105.75$$ $$1.10x + 94.75 = 105.75$$ 7. Solve for $x$: $$1.10x = 105.75 - 94.75$$ $$1.10x = 11$$ $$x = \frac{11}{1.10} = 10$$ 8. Find $y$: $$y = 25 - 10 = 15$$ 9. **Interpretation:** Melody should use 10 bags of M&M’s and 15 bags of Reese’s Pieces. 10. **Recommendation:** This mix meets the total bag count and average cost requirements.