The average (mean) of a and b is 10. The average of b and 10 is 1/2 of c. What is the average of a and c?

"The average (mean) of a and b is 10" ---> (a+b)/2 = 10 or a+b=20

" The average of b and 10 is 1/2 of c" ---> (b+10)/2 = c/2 or b+10=c or
c-b=10

add:
a+b=20
c-b=10

a+c=30

so the average of a+c or (a+c)/2 = 15