## 131. Math Puzzle $4 / 76$

At the air rifle shooting during the Pioneer afternoon, Marion took third place. Beate won, scoring four rings more than Marion and two rings more than Ina.

Marion achieved 4/5 of the total possible rings. If you add the rings scored by the three girls, you get the 21/2 times the total possible rings.

What is this total number? What ring scores did the three girls achieve?
Let $n$ be the number of rings a shooter can achieve at most. Then, Marion gets $\frac{4}{5} n$, Beate gets $\frac{4}{5} n+4$, and Ina gets $\frac{4}{5} n+2$ rings.

$$
\frac{12}{5} n+6=\frac{5}{n}, \quad n=60
$$

A shooter achieved 66 rings. Beate scored 52, Ina 50, and Marion 48 rings.