Salt in sandbox as weed control?

I have a very large sand box for my children, which surrounds their slide and swing set.  It's approximately 12 foot by 24 foot.  The sand is over a weed membrane, with a sand depth of about 6 inches.  It is surrounded by a poured cement border (solid divide between sand and surrounding soil for about six inches deep).  The sandbox is next to our 'wild' area of tall grasses and various weeds.. which seed and blow into the sand.  It's been a constant battle with the weeds in the sand.. which I"m loosing.  Last year I sprayed with Roundup occasionally, when I couldn't keep up with pulling by hand.  But the boys play out their daily, so it's difficult to keep them off there for approximately three days after each spraying.  And Roundup is darn expensive.  Most of the weeds currently are grasses, as I pull out the nastier ones by hand when I see them.  

Could I go out there with a large container of table salt (or rock salt?) and sprinkle it over the sand, then water in with the hose?  What sort of amount per square foot would be likely to kill off weeds, but not be excessive?  I realize it will make the ground sterile for some while to come.. but that's sort of the point.