## 5. Height

In a certain class, the average height of all twenty-two students was $163.5 \mathrm{~cm}$. Soon, one more student was enrolled in the class, and the average height increased by $0.3 \mathrm{~cm}$. The very next day, one student dropped out of the class, and the average height increased again, this time by $0.4 \mathrm{~cm}$. How tall, in centimeters, was the student who dropped out?

## Result: $\quad 155$
## First solution.

Let $a$ be the sum of the heights of twenty-two students.

It holds that $\frac{a}{22}=163.5$, so $a=163.5 \cdot 22$, which means $a=3597$.

Let $y$ be the height of the enrolled student.

Then the sum of the heights of all twenty-three students is $y+3597$, and the average height is $163.5+0.3=163.8$, so we have: $\frac{y+3597}{23}=163.8$.

From this, we get $y+3597=163.8 \cdot 23=3767.4$.

Let $x$ be the height of the student who withdrew.

Then the sum of the heights of the remaining twenty-two students is $3767.4-x$,

and their average height is $163.8+0.4=164.2$.

Therefore, it holds that: $\frac{3767.4-x}{22}=164.2$, so

$3767.4-x=164.2 \cdot 22=3612.4, x=3767.4-3612.4=155$

The height of the student who withdrew is $155 \mathrm{~cm}$.