The old liar

Three friends, Adam, Beth, and Cleo, are sitting together and talking. Together they are 150 years old.

Adam: In 9 years, you two together will be as old as we three together are right now.

Beth: Ten years ago, the sum of your both ages was my age right now.

Cleo: Beth, 10 years ago I was twice your age.

If we know that the oldest, and only the oldest of the three is a liar, can you tell the ages of the three persons?

Erich Prisner, August 2003