My home is 11 years old, and I've owned it for the last 9. The grout was already breaking up in a few places in the entryway when I bought it, so I know that it probably wasn't installed properly. I'm also pretty sure that the tile installer forgot to seal the entryway grout, because we're not having any problems with identical tile and grout in the "powder room", but the entryway grout has been grungy from day one. I've spent hours scrubbing it, to no avail.
I'd like to replace the broken grout and then use a colorant over all of it to hide the dirt, and avoid having to match the grout color. Is this practical? Or should I plan on redoing all of it? I saw another answer here that recommended using a grout saw to scrape off the top layer of grout to get it clean; is that better than coloring over the stains?
If it matters, the tile is 12" square, the cheapest stuff you can find, with about 1/4" grout lines. This was the builder's default material so you know there is no quality to be found here, but I'd rather not have to replace it all. The tiles themselves are in good condition.