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Yes, you can put new mulch over old mulch, since it’s decomposable. The only reason you should remove old mulch before laying new mulch would be to maintain a certain aesthetic. 

Replace organic mulch every one to two years, depending on the variety. Wood chips and straw, for example, will last a couple of years, while grass clippings and pine needles need replacing every several months. Inorganic mulch—such as rock and rubber chips—can stay in place for up to four years, depending on erosion and general garden upkeep. 

The least costly way to keep grass from growing is also the most labor-intensive: regular weeding. Pull out grass blades as you see them pop up through the soil in areas where they’re unwanted. Another cost-effective way to keep grass from growing is by spreading a thick layer of mulch on the area as this will suffocate the grass.

Each bag of mulch includes 2 cubic feet of mulch. And since a cubic yard is about 27 cubic feet of materials, you'll need 14 bags of mulch to have enough to cover a cubic yard. The right amount of mulch for your yard, however, depends on the depth of the mulch, the type of mulch you choose, and your desired look.