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Lexi Salzman has a large rectangular vegetable garden measuring 12 ft by 22 ft. An employee at the local nursery recommended putting down mulch 2 in. thick to prevent weeds from growing. Each bag of mulch covers 2 cubic feet. How many bags should Lexi purchase for her vegetable​ garden?

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To determine how many bags of mulch Lexi should purchase, we need to calculate the volume of mulch required for her garden.

  1. Calculate the area of the garden in square feet: \[ \text{Area} = \text{Length} \times \text{Width} = 12 , \text{ft} \times 22 , \text{ft} = 264 , \text{ft}^2 \]

  2. Convert the thickness of the mulch from inches to feet: Since there are 12 inches in a foot, a depth of 2 inches is: \[ \text{Thickness in feet} = \frac{2 , \text{in}}{12 , \text{in/ft}} = \frac{1}{6} , \text{ft} \approx 0.1667 , \text{ft} \]

  3. Calculate the volume of mulch required: \[ \text{Volume} = \text{Area} \times \text{Thickness} = 264 , \text{ft}^2 \times \frac{1}{6} , \text{ft} = 44 , \text{ft}^3 \]

  4. Calculate the number of bags of mulch needed: Each bag covers 2 cubic feet, so: \[ \text{Number of bags} = \frac{\text{Volume}}{\text{Volume per bag}} = \frac{44 , \text{ft}^3}{2 , \text{ft}^3/\text{bag}} = 22 , \text{bags} \]

Therefore, Lexi should purchase 22 bags of mulch.