Why is a differential white blood cell count more valuable than a total white blood cells count when trying to pin down the specific source of pathology?

A total white blood count gives a single number - how many white blood cells were present per milliliter of sample. A differential white blood count breaks the number down among the different white blood cell types - neutrophil, lymphocyte, monocyte, basophil, eosinophil. Different white blood cells will respond to different types of pathology - neutrophils are associated with bacterial infections, eosinophils with parasite infestation, monocytes with chronic infections, etc.