3. Shoji invested $\$ 7000$, part at $9 \%$ interest and part at $6 \%$ interest. The interest obtained from the $6 \%$ investment was half of the interest obtained from the $9 \%$ investment. How much was invested at each rate?

Step 1 ：Let the amount invested at 9% be \(x\) and the amount invested at 6% be \(y\).

Step 2 ：Set up the system of equations: \[\begin{cases} x + y = 7000 \\ 0.06y = 0.5(0.09x) \end{cases}\]

Step 3 ：Solve the system of equations to find the values of \(x\) and \(y\).

Step 4 ：\(x = 4000\) and \(y = 3000\)

Step 5 ：\(\boxed{\text{Shoji invested $4000 at 9% interest and $3000 at 6% interest.}}\)