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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?

  1. $81$
  2. $81.5$
  3. $82$
  4. $84.5$
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