A way to make my grapes last longer and not mold??

I absolutely love grapes, I buy a big bag of them every time I do my grocery shopping. I eat them a lot..but my problem is that within a few days a few on the bottoms are starting to mold, so I take out the good ones and put them in a container and in the fridge they go. So if I just did that every time I bought grapes (put them into a container and put them in the fridge) would they last longer?