let the marks of the students in class 1 be
[tex]m_1, m_2, ....., m_1_2[/tex]
the average of these 12 marks is 90, so
[tex]\frac{m_1+ m_2+ .....+ m_1_2}{12}=90 [/tex]
which means
[tex]m_1+ m_2+ .....+ m_1_2=90*12=1080[/tex]
similarly, let [tex]n_1, n_2, ....., n_2_0[/tex] be the marks of the students in the second class,
so [tex] \frac{n_1+ n_2+ ..... n_2_0}{20}=80 [/tex]
which means [tex]n_1+ n_2+ ..... n_2_0=80*20=1600[/tex]
The 32 students averaged:
[tex] \frac{(m_1+ m_2+ .....+ m_1_2)+(n_1+ n_2+ ..... n_2_0)}{12+20}= \frac{1080+1600}{32}= \frac{2680}{32}= 83.75[/tex]
