Question 60
Randall proposes a new temperature system called Felsius temperature with the following conversion between Felsius $\{ \}^{\circ} E$, Celsius $\{ \}^{\circ} C$, and Fahrenheit $\{ \}^{\circ} F$:
$$
\{ \}^{\circ} E = \frac{7 \times \{ \}^{\circ} C}{5} + 16 = \frac{7 \times \{ \}^{\circ} F - 80}{9}.
$$
For example, $0^{\circ} C = 16^{\circ} E$. Let $x, y, z$ be real numbers such that $x^{\circ} C = x^{\circ} E$, $y^{\circ} E = y^{\circ} F$, $z^{\circ} C = z^{\circ} F$. Find $x + y + z$.
$$
\{ \}^{\circ} E = \frac{7 \times \{ \}^{\circ} C}{5} + 16 = \frac{7 \times \{ \}^{\circ} F - 80}{9}.
$$
For example, $0^{\circ} C = 16^{\circ} E$. Let $x, y, z$ be real numbers such that $x^{\circ} C = x^{\circ} E$, $y^{\circ} E = y^{\circ} F$, $z^{\circ} C = z^{\circ} F$. Find $x + y + z$.