Answer
$\$1700$ at $5\%$ and $\$ 1300$ at $8\%$.
Work Step by Step
Let the amount invested at $5\%$ be $x$.
and the amount invested at $8\%$ be $y$.
Total amount $x+y=\$3000$...... (1)
and total interest $0.05x+0.08y=\$189$......(2)
Multiply equation (1) by $-0.05$.
$-0.05x-0.05y=-0.05\cdot \$3000$
$-0.05x-0.05y=-\$150$ ......(3)
Add equation (2) and (3).
$0.05x+0.08y-0.05x-0.05y=\$189-\$150$
Add like terms.
$0.03y=\$39$
Divide both sides by $0.03$.
$\frac{0.03y}{0.03}=\frac{\$39}{0.03}$
Simplify.
$y=\$1300$
Plug the value of $y$ into equation (1).
$x+\$1300=\$3000$
Subtract $\$1300$ from both sides.
$x+\$1300-\$1300=\$3000-\$1300$
Simplify.
$x=\$1700$.
