On friday vance gave 11 more flu shots than mike did. together they gave 53 flu shots. how many flu?

Mike gave x flu shots. Vance gave 11 more than Mike; that adds up to 11 + x for Vance.
Together they gave 53 flu shots:
11 + x + x = 53
11 + 2x = 53
2x = 42
x = 21

21 + 11 = 32 shots by Vance.
53 - 32 = 21 shots by Mike.