I am thinking about taking this cat that my grandparents have that they don't want anymore, but I need to know how long cats usually live before I can have the cat.

A strong genetic background for longevity can't be discounted. Given proper care, nutrition, and regular veterinary visits, a cat kept indoors can live as long as 21 years or more. (The average age of cats is 12-15 years) This is, of course, barring any serious medical conditions or untimely accidents.