Solution — 2019 Question 1 Simultaneous Linear Equations

Let $a$ be the price of a Style $A$ television, $b$ be the price of a Style $B$ television, and $c$ be the price of a Style $C$ television.

From last month’s sales:

\begin{matrix} 22 a + 16 b + 8 c & = 96 480 & (1) \end{matrix}

The income from Style $A$ sales was $$ 3120$ more than the income from Style $B$ sales:

\begin{matrix} 22 a - 16 b & = 3120 & (2) \end{matrix}

From this month’s sales (selling 2 more of each style with an increase of $$ 13260$ in total income):

\begin{matrix} 24 a + 18 b + 10 c & = 109 740 & (3) \end{matrix}

Solving with a GC,

\begin{matrix} a & = 1800 \end{matrix}

\begin{matrix} b & = 2280 \end{matrix}

\begin{matrix} c & = 2550 \end{matrix}

The price of a Style $B$ television is $$ 2,280 ∎$