HMMT 2018 U5

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 $x+y+z$.