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Three math classes; $\text{X, Y},$ and $\text{Z},$ take an algebra test.

- The average score in class $\text{X}$ is $83.$
- The average score in class $\text{Y}$ is $76.$
- The average score in class $\text{Z}$ is $85.$
- The average score of all students in classes $\text{X}$ and $\text{Y}$ together is $79.$
- The average score of all students in classes $\text{Y}$ and $\text{Z}$ together is $81.$

What is the average for all three classes?

- $81$
- $81.5$
- $82$
- $84.5$