On every weekday morning, a theatre admits 20 adults and 40 children for a show. On every weekday afternoon, the theatre admits 30 adults and 30 children. This information can be represented by the matrix $A = \begin{pmatrix}20 & 40\\[4pt]30 & 30\end{pmatrix}$ where the columns are Adults and Children and the rows are Morning and Afternoon. On every weekend morning, the theatre admits 30 adults and 60 children for the show. On every weekend afternoon, the theatre admits 35 adults and 55 children.

1. (a)

   Represent the number of people admitted to the show on a day in the weekend by a matrix B.

   Answer B = ...

2. (b)

   Evaluate the matrix C = 5A + 2B.

   Answer C = ...

3. (c)

   State what the elements of C represent.

   Answer ...

   ...

4. (d)

   The admission fee for an adult is $25 and for a child is$12.

   1. (i)

      Evaluate the matrix $D = C\begin{pmatrix}25 \\ 12\end{pmatrix}$.

      Answer D = ...

   2. (ii)

      Evaluate the matrix $E = \dfrac{1}{7}\begin{pmatrix}1 & 1\end{pmatrix}D$.

      Answer E = ...

   3. (iii)

      State what the elements of E represent.

      Answer ...

      ...