If M and Z are the number of free throws each makes, then M/Z=3/5, so M=3Z/5.
Also Z=M+10.
Now we substitute for Z:
M=3Z/5=3(M+10)/5.
Multiply through by 5: 5M=3M+30, 2M=30, M=15 and Z=15+10=25.
Mike made 15 free throws.
CHECK
M/Z=15/25=3/5 OK
Z=M+10; 25=15+10 OK