Solution — 2020 Question 3 Simultaneous Linear Equations

(a)

Let $p,$ $l$ and $t$ be the prices of a phone, a laptop and a TV respectively.

\begin{matrix} l & = 2 p \\ 2 p & = l \\ 2 p - l & = 0 & (1) \end{matrix}

\begin{matrix} 3 p + 2 l + 8 t & = 24 120 & (2) \end{matrix}

\begin{matrix} l & = p + 2 t - 640 \\ p + 2 t - 640 & = l \\ p - l + 2 t & = 640 & (3) \end{matrix}

Solving equations (1), (2) and (3) with a GC,

$p = 1960, t = 1300, l = 3920$

Therefore, the price of a phone is $$ 1960 ∎$

(b)

\begin{matrix} Amount Mia has to pay \\ = 0.9 (0.2 (80) (1960) + 0.2 (80) (3920) + 0.6 (80) (1300)) \\ = $ 140 832 ∎ \end{matrix}