Solution — 2022 Question 1 Simultaneous Linear Equations

Let $P, Q$ and $R$ represent the cost of one Type $P, Q$ and $R$ radio respectively

$\begin{matrix} 12 P + 16 Q + 9 R & = 1290.60 & (1) \end{matrix}$

$\begin{matrix} 3 P & = 4 Q \\ 3 P - 4 Q & = 0 & (2) \end{matrix}$

$\begin{matrix} 15 R & = 10 P + 10 Q + 46.50 \\ - 10 P - 10 Q + 15 R & = 46.5 & (3) \end{matrix}$

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

$P = 36.60, Q = 27.45, R = 45.80$

$Cost of one Type R radio = $ 45.80 ∎$