1. Calculate the area of the garden:
20 \, \text{ft} \times 24 \, \text{ft} = 480 \, \text{ft}^2
2. Convert the thickness of the topsoil layer from inches to feet:
3 \, \text{inches} = 0.25 \, \text{ft}
3. Calculate the total volume required in cubic feet:
480 \, \text{ft}^2 \times 0.25 \, \text{ft} = 120 \, \text{ft}^3
4. Convert the volume to cubic yards:
\frac{120 \, \text{ft}^3}{27 \, \text{ft}^3/\text{yd}^3} \approx 4.444 \, \text{yd}^3
5. Round up to the nearest 1/4 cubic yard since the store sells in these increments:
Needed volume is 4.5 cubic yards.