A circus sells three different types of tickets: family \((F)\), adult \((A)\) and child \((C)\).
The cost of admission, in dollars, for each ticket type is presented in matrix \(N\) below.
\(N=\begin{bmatrix}
36 \\
15 \\
8
\end{bmatrix}\begin{aligned}
F \\
A \\
C
\end{aligned}\)
The element in row \(i\) and column \(j\) of matrix \(N\) is \(n_{i j}\).
- Which element shows the cost for one child ticket? (1 mark)
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- A family ticket will allow admission for two adults and two children.
- Complete the matrix equation below to show that purchasing a family ticket could give families a saving of $10. (1 mark)
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\(\displaystyle{\begin {bmatrix} 0 &2&2 \end {bmatrix} \times N - \begin{bmatrix} \rule{1cm}{0.25mm} & \rule{1cm}{0.25mm} & \rule{1cm}{0.25mm} \end {bmatrix} \times N = \left[ 10\right]}\)
- On the opening night, the circus sold 204 family tickets, 162 adult tickets and 176 child tickets.
- The owners of the circus want a 3 × 1 product matrix that displays the revenue for each ticket type: family, adult and child.
- This product matrix can be achieved by completing the following matrix multiplication.
\(K \times N=\begin{bmatrix}
7344 \\
2430 \\
1408
\end{bmatrix}\)
- Write down matrix \(K\). (1 mark)
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