180. Math Puzzle $5 / 80$

In a seventh-grade class, the following result was achieved in a physics test:



Half of the students were able to get a grade of Two. One-sixth of the students showed very good performance. One-fifth of the tests received a grade of Three. Four students performed only inadequately.

a) How many students took the test?

b) What was the average grade achieved?
a) The number of students who participated in the physics exam is calculated using the following equation:

$$
\frac{x}{2}+\frac{x}{6}+\frac{x}{5}+4=x
$$

The solution to this equation is $x=30$ students.

b) The average grade was then easy to determine.

$$
\text { Grades: } \begin{array}{rrrrr}
1 & 2 & 3 & 4 & 5 \\
\hline 5 & 15 & 6 & 0 & 4
\end{array}
$$

The average grade was: $(1 \cdot 5+2 \cdot 15+3 \cdot 6+5 \cdot 4)=2.43 \approx 2.4$.