Answer
$x=30000,$
$y=30000,$
$z=40000$
Work Step by Step
Short-term=$4\%$
Intermediate=$5\%$
Long-term=$6\%$
let $x$ denote the amount he invests in short-term,
let $y$ denote the amont he invests in Intermediate
let $z$ denote the amount he invests in long-term bond.
Thus, $x+y+z=100,000,$ denotes a formula the amount he invests and $0.04x+0.05y+0.06z=100,000\times0.051$ denotes a formula the amount it returns in a year.
Whereas, $x=y$.
$\begin{cases}
2y+z=100000\\
0.09y+0.06z=5100\\
\end{cases}$
Multiplying Equation 2 by -22.22.. and adding it to Equation 1.
$\begin{cases}
2y+z=100000\\
-2y-1.33z=-113333.333\\
-- -- -- -- --\\
-0.333z=-13333.333
\end{cases}$
Thus, $z=40000$. Substituting it back in, $2y+40000=100000, y=30000$. Since $x=y, x=30000$.
