2026 RSS P2 Q3

Secondary 4

8 marks

During the World Cup, merchandise such as jerseys and caps are sold.
Game 1 sold 12 000 jerseys and 4000 caps.
Game 2 sold 9000 jerseys and 5600 caps.
Game 3 sold 11800 jerseys and 3000 caps.
The number sold, in thousands, are shown in the matrix
$\mathbf W=\begin{pmatrix}12&4\\9&5.6\\11.8&3\end{pmatrix}$.
A jersey is priced at $\$80$ and a cap at $\$30$.
1. Represent the price of the merchandise in a $2\times1$ column matrix $\mathbf P$.[1]
2. Evaluate the matrix $\mathbf T=\mathbf W\mathbf P$.[2]
3. Explain what the elements in $\mathbf T$ represent.[1]
The remaining stock consists of 7000 jerseys and 8000 caps.
After a storewide discount was applied, the sale of the remaining stock is represented by the matrix equation
$d\begin{pmatrix}7&8\end{pmatrix}\begin{pmatrix}80&0\\0&30\end{pmatrix}=\begin{pmatrix}448&192\end{pmatrix}$,
where $d$ is a constant.
Find the percentage discount given by the store.[4]

Solution:

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Answer:(a)(i) $\mathbf P=\begin{pmatrix}80\\30\end{pmatrix}$ (ii) $\mathbf T=\begin{pmatrix}1080\\888\\1034\end{pmatrix}$ (iii) Revenues in thousands of dollars for Games 1–3. (b) $20\%$

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