Alvin is 11 years older than elga. the sum of their ages is 81 . what is elga's age?

Let A = Alvin, let E = Elga. We use these to set up a system of equations. 

A + E = 81
E + 11 = A

We can rewrite that equation to be:

A + E = 81
- A + E = - 11

Now combine like terms:

2E = 70
E = 35

Plug back in to find A.

E + 11 = A
35 + 11 = A
46 = A

Alvin is 46 years old; Elga is 35 years old.