Biology test

Peter Šťastný did not manage to study for the biology test due to urgent matters. In the test, for every correctly solved task there were 10 points, for a wrongly solved task 5 points were subtracted, one could also not answer, for which there were 0 points. Peter, however, relied on his lucky name (Šťastný means "lucky") and for all the tasks which he could not solve, he guessed the correct answer. He got 80 points from the test. How many of his answers were correct, if the test had 20 questions?

Final Answer:

q =  5

Step-by-step explanation:

$$\begin{gathered} 10s-5n+0z=80 \\ s+n+z=20 \\ {n}_1=0,s_1=8,z_1=12 \\ {n}_2=2,s_2=9,z_2=9 \\ {n}_3=4,s_3=10,z_3=6 \\ {n}_4=6,s_4=11,z_4=3 \\ {n}_5=8,s_5=12,z_5=0 \\ q=5 \end{gathered}$$

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