#6. Let the number of adults is a and the number of children is c.
The total number of people is 42,
a+c=42......(1).
The sales made by selling tickets is $396,
12a+8c=396.....(2)
Thus, the above two equation gives the required system of equation for the problem.
#7.
The system of equation can be solved as by substituting the value of c from (1) in (2),
[tex]\begin{gathered} 12a+8(42-a)=396_{} \\ 4a=396-336 \\ 4a=60 \\ a=15 \end{gathered}[/tex]Thus, a=15.
Now susbstituting the value of a in equaiton (1),
[tex]\begin{gathered} 15+c=42 \\ c=42-15 \\ c=27 \end{gathered}[/tex]#8.
Thus, number of adults in the therater is 15 and number of children in the theatre is 27.
