Class grade average

There are 30 students in the class. Five had a mark three — other twos and ones. The average grade was 1.9. How many students got mark one?

Final Answer:

a =  8

Step-by-step explanation:

$$\begin{gathered} a+b+c=30 \\ c=5 \\ 1.9=\frac{1\cdot a+2\cdot b+3\cdot c}{30} \\ 1.9\cdot 30=a+2b+3\cdot 5 \\ 57=a+2b+15 \\ 42=a+2b \\ 42=a+2b \\ a+b=25 \\ 42=a+2\cdot b \\ a+b=25 \\ a+2b=42 \\ Row2-Row1\to Row2 \\ -b=-17 \\ b=\frac{-17}{-1}=17 \\ a=42-2b=42-2\cdot 17=8 \\ a=8 \\ b=17 \\ \text{ Verifying Solution: } \\ n=a+b+c=8+17+5=30 \\ \mu =\frac{1\cdot a+2\cdot b+3\cdot c}{a+b+c}=\frac{1\cdot 8+2\cdot 17+3\cdot 5}{8+17+5}=\frac{19}{10}=1\frac{9}{10}=1.9 \end{gathered}$$

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