Step-by-step explanation:
Let a be the total score of Div. A
Let b be the total score of Div. B
given,
[tex] \frac{a}{15} - \frac{b}{20} = 2[/tex]
as equation 1.
and
[tex]b - a = 160 \\ - a + b = 160[/tex]
as equation 2.
Now multiply equation 2 by 1/20 to eliminate b to solve for a.
[tex] ( - a)( \frac{1}{20} ) + (b)( \frac{1}{20} ) = ( \frac{1}{20} )(160) \\ - \frac{a}{20} + \frac{b}{20} = 8[/tex]
take this new equation as equation 3.
now we will use equation 1 + equation 3 to eliminate b to solve for a.
[tex] ( \frac{a}{15} + ( - \frac{a}{20} )) + ( - \frac{b}{20} + \frac{b}{20} ) = 2 + 8 \\ \frac{a}{60} = 10 \\ a = 60 \times 10 \\ = 600[/tex]
Div.A total score = 600
Average Score = Total Score / Number of students.
[tex] \frac{600}{15} \\ = 40[/tex]
