1. **State the problem:** Megan has two boxes with given dimensions. We need to find the volume of each box and determine which box has the greater volume to decide which one she should use. 2. **Formula for volume of a rectangular box:** $$\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}$$ 3. **Convert mixed numbers to improper fractions:** - Box A length: $6 \frac{1}{2} = \frac{13}{2}$ yards - Box A height: $15 \frac{1}{2} = \frac{31}{2}$ yards - Box B width: $3 \frac{1}{4} = \frac{13}{4}$ yards - Box B height: $12 \frac{1}{2} = \frac{25}{2}$ yards 4. **Calculate volume of Box A:** $$V_A = \frac{13}{2} \times 3 \times \frac{31}{2}$$ Multiply numerator and denominator: $$V_A = \frac{13 \times 3 \times 31}{2 \times 1 \times 2} = \frac{1209}{4}$$ Convert to mixed number: $$1209 \div 4 = 302 \text{ remainder } 1 \Rightarrow 302 \frac{1}{4}$$ 5. **Calculate volume of Box B:** $$V_B = 7 \times \frac{13}{4} \times \frac{25}{2}$$ Multiply numerator and denominator: $$V_B = \frac{7 \times 13 \times 25}{1 \times 4 \times 2} = \frac{2275}{8}$$ Convert to mixed number: $$2275 \div 8 = 284 \text{ remainder } 3 \Rightarrow 284 \frac{3}{8}$$ 6. **Compare volumes:** Box A volume = $302 \frac{1}{4}$ cubic yards Box B volume = $284 \frac{3}{8}$ cubic yards 7. **Conclusion:** Box A has the greater volume. **Final answer:** Box A has a volume of $302 \frac{1}{4}$ and Box B has a volume of $284 \frac{3}{8}$. She should choose Box A because it has the greater volume.