In the primary

In a primary school every year a knowledge competition is organised, in which each competitor can get at most 15 points. This year the average point achievement of the competitors, rounded to tenths, was 10.4. Jožko realised after the competition that some questions he had read wrongly and answered something else. He could thus have had 4 points more, and the average point achievement rounded to tenths would by this have increased to 10.6. Determine how many competitors at the least and at the most could have competed this year.

Final Answer:

n =  20

Step-by-step explanation:

$$\begin{gathered} (10.4\cdot (n-1)+j)/n=10.4 \\ (10.4\cdot (n-1)+j+4)/n=10.6 \\ 10.4\cdot (n-1)+j=10.4\cdot n \\ 10.4\cdot (n-1)+j+4=10.6\cdot n \\ 10.4\cdot n+4=10.6\cdot n \\ 0.2n=4 \\ n=\frac{4}{0.2}=20 \\ n=20 \end{gathered}$$

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