Answer
Invest:
$\$ 14,000$ in the 5% account,
$\$ 6,000$ in the 8% account.
Work Step by Step
If she invests
x dollars in the first account, paying 5% interest,
y dollars in the second account, paying 8% interest,
then
$x+y=20,000$ and
$0.05x+0.08y=1180\qquad\times 100$
$5x+8y=118,000$
We have the system
$\left\{\begin{array}{ll}
x+y=20,000 & /\times(-5)\\
5x+8y=118,000 &
\end{array}\right. $
(eliminates x)
$\left\{\begin{array}{ll}
-5x-5y=-100,000 & \\
5x+8y=118,000 & /add
\end{array}\right.$
$3y=18,000\qquad/\div 3$
$y=6000$
Back-substitute:
$x+y=20,000$
$x+6000=20,000$
$x=14,000$
Invest:
$\$ 14,000$ in the 5% account,
$\$ 6,000$ in the 8% account.
