Represented

The children of class 5 A wrote a maths test. The class had 29 children. After marking, there were two more grade 1 s than grade 5 s; grade 3 occurred three times; grade 2 represented twice the number of grade 1 s; grade 4 did not occur. How many students received each grade from 1 to 5? What is the class average grade?

Final Answer:

a =  7
b =  14
c =  3
d =  0
e =  5
x =  2.3793

Step-by-step explanation:

$$\begin{gathered} d=0 \\ c=3 \\ b=2\cdot a \\ a=2+e \\ a+b+c+d+e=29 \\ b=2\cdot a \\ a=2+e \\ a+b+3+0+e=29 \\ 2a-b=0 \\ a-e=2 \\ a+b+e=26 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 0.5b-e=2 \\ Row3-\frac{1}{2}\cdot Row1\to Row3 \\ 1.5b+e=26 \\ Pivot:Row2\leftrightarrow Row3 \\ Row3-\frac{0.5}{1.5}\cdot Row2\to Row3 \\ -1.333e=-6.667 \\ e=\frac{-6.66666667}{-1.33333333}=5 \\ b=\frac{26-e}{1.5}=\frac{26-5}{1.5}=14 \\ a=\frac{0+b}{2}=\frac{0+14}{2}=7 \\ a=7 \\ b=14 \\ e=5 \end{gathered}$$

$x=\frac{1\cdot a+2\cdot b+3\cdot c+4\cdot d+5\cdot e}{a+b+c+d+e}=\frac{1\cdot 7+2\cdot 14+3\cdot 3+4\cdot 0+5\cdot 5}{7+14+3+0+5}=\frac{69}{29}=2\frac{11}{29}=2.3793$

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