Average mark

In the 6th class, the average half-year mark in physics was 1.7. At the end of the year, Matthew improved his grade from 2 to 1, Ivana from 3 to 2, and Elena from 4 to 2. Paul's grade worsened from 3 to 4. The average mark of the whole class thus improved by 0.1. How many children in this class could have a physics mark one (the best) at the end of the year maximally?

Final Answer:

n =  30
a =  12

Step-by-step explanation:

$$\begin{gathered} p_1=1.7 \\ {p}_2=p_1-0.1=1.7-0.1=\frac{8}{5}=1\frac{3}{5}=1.6 \\ n\cdot p_1=p_2\cdot n+(2-1)+(3-2)+(4-2)+(3-4) \\ n\cdot 1.7=1.6\cdot n+(2-1)+(3-2)+(4-2)+(3-4) \\ 0.1n=3 \\ n=\frac{3}{0.1}=30 \\ n=30 \end{gathered}$$

$$\begin{gathered} p_2\cdot n=a\cdot 1+(n-a)\cdot 2 \\ 1.6\cdot 30=a\cdot 1+(30-a)\cdot 2 \\ a=12 \end{gathered}$$

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