Answer
$x=28000,$
$y=8000,$
$z=14000$
Work Step by Step
Account paying simple interest=$3\%$
Account paying simple interest=$5.5\%$
Account paying simple interest=$9\%$
let $x$ denote the account paying $3\%$,
let $y$ denote the account paying $5.5\%$,
let $z$ denote the account paying $9\%$.
Thus, $x+y+z=50,000,$ denotes a formula the amount she invests and $0.03x+0.05.5y+0.09z=2540$ denotes a formula the amount it returns in a year.
Whereas, $x=2z$.
$\begin{cases}
y+3z=50000\\
0.055y+0.15z=2540\\
\end{cases}$
Multiplying Equation 2 by -20 and adding it to Equation 1.
$\begin{cases}
y+3z=50000\\
-0.1y-3z=-50800\\
-- -- -- -- --\\
-0.1y=-800
\end{cases}$
Thus, $y=8000$. Substituting it back in, $8000+3z=50000, z=14000$. Since $x=2z, x=28000$.
