Mug Capacity Ed6545

1. **State the problem:** We are given that a mug is $\frac{2}{7}$ full and contains $\frac{5}{7}$ of a cup of water. We need to find the total capacity of the mug. 2. **Formula used:** If the mug is $\frac{2}{7}$ full and contains $\frac{5}{7}$ cups of water, then the capacity $C$ of the mug satisfies: $$\frac{2}{7} \times C = \frac{5}{7}$$ 3. **Solve for $C$:** Multiply both sides by $\frac{7}{2}$ to isolate $C$: $$C = \frac{5}{7} \times \frac{7}{2}$$ 4. **Simplify the expression:** $$C = \frac{5 \cancel{7}}{\cancel{7} \times 2} = \frac{5}{2}$$ 5. **Interpretation:** The capacity of the mug is $\frac{5}{2}$ cups, which is equal to $2.5$ cups. **Final answer:** The capacity of the mug is $2.5$ cups.