Question

Movie tickets are in $12 dollars for adults and $8 for children. A showing of 'Godzilla versus King Kong' had 42 people in it and the theater made $396 in ticket sales.6) write 'a' system of equation that represents the situation. Let a represent the adults 'c' represent the children.7) solve the system you wrote in #68) interpret your solution in the context problem.

Answer 1

#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),

`\begin{gathered} 12a+8(42-a)=396_{} \\ 4a=396-336 \\ 4a=60 \\ a=15 \end{gathered}`

Thus, a=15.

Now susbstituting the value of a in equaiton (1),

`\begin{gathered} 15+c=42 \\ c=42-15 \\ c=27 \end{gathered}`

#8.

Thus, number of adults in the therater is 15 and number of children in the theatre is 27.