Why an egg sinks in water but not in salt water

When salt is added to water, salt, which is more dense than water, will increase the density of water.

Now, I will explain why the egg sunk in tap water but floated in salt water.
An egg is more dense than water, so it floats. However, when salt is added, the density of the water increases so it becomes more dense than the egg, thus, the egg floats.