Mathematicians 11761

The top five mathematicians in the class took on the teacher's help in calculating the paper's average grade. They dictated the following results:
Mischa: "I came up with 3.30. "
Dasha: "That's weird because it worked out precisely at 3.45. "
Jana: "You probably can't count because I think it's 2.94. And I also didn't round. "
Roman: "I checked it three times, and I got 3.44. Damian: "Interesting, I only got 2.60. "
Thirty students wrote that no one received a five, and only two students received a four. One of the results was correct. Who dictated the right result?

Correct answer:

x = DAMIAN

Step-by-step explanation:

$$\begin{gathered} n=30 \\ \frac{1\cdot a+2\cdot b+3\cdot (n-a-b-2)+4\cdot 2}{n}=p \\ 1\cdot a+2\cdot b+3\cdot (30-a-b-2)+4\cdot 2=n\cdot p \\ n\cdot p\in N \\ MISO:1\cdot a+2\cdot b+3\cdot (30-a-b-2)+4\cdot 2=99 \\ a,b\notin N \\ DASA:1\cdot a+2\cdot b+3\cdot (30-a-b-2)+4\cdot 2=103.5 \\ JANA:1\cdot a+2\cdot b+3\cdot (30-a-b-2)+4\cdot 2=88.2 \\ ROMAN:1\cdot a+2\cdot b+3\cdot (30-a-b-2)+4\cdot 2=103.2 \\ DAMIAN:1\cdot a+2\cdot b+3\cdot (30-a-b-2)+4\cdot 2=78 \\ {a}_1=0,b_1=14 \\ {a}_2=1,b_2=12 \\ {a}_3=2,b_3=10 \\ {a}_4=3,b_4=8 \\ {a}_5=4,b_5=6 \\ {a}_6=5,b_6=4 \\ {a}_7=6,b_7=2 \\ {a}_8=7,b_8=0 \\ x=DAMIAN \end{gathered}$$

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