Solution — 2018 Question 3 Simultaneous Linear Equations

(a)

Let $a$ be the monthly salary of an accountant, $b$ be the monthly salary of a financial adviser, and $c$ be the monthly salary of a consultant.

From the given information:

\begin{matrix} 5 a + 12 b + 8 c & = 294 100 & (1) \end{matrix}

\begin{matrix} 9 a + 7 b + 3 c & = 270 100 & (2) \end{matrix}

\begin{matrix} 3 a + 6 b & = 122 700 & (3) \end{matrix}

Solving with a GC,

\begin{matrix} a & = 18 500 \end{matrix}

\begin{matrix} b & = 11 200 \end{matrix}

\begin{matrix} c & = 8400 \end{matrix}

\begin{matrix} Cost of training one financial advisor & = $ 11,200 ∎ \end{matrix}

(b)

\begin{matrix} Cost of one accountant and financial advisor after increase \\ = 1.1 (18 500 + 11 200) \\ = 32 670 \end{matrix}

\begin{matrix} \frac{200 000}{32 670} & = 6.1218 \end{matrix}

\begin{matrix} Greatest number of accounts & = 6 ∎ \end{matrix}