HW Score: \( 42.86^{\%} \) If \( \$ 9,000 \) is invested in a bank that pays \( 3 \% \) interest, how much more must be invested in bonds at \( 7 \% \) to earn \( 5 \% \) on the total investment?

To determine how much more must be invested in bonds at \( 7\% \) to achieve an overall \( 5\% \) return on a total investment combined with a bank investment at \( 3\% \), we first need to calculate the interest earned from the initial \( \$ 9,000 \) investment. The annual interest from the bank is: \[ \text{Interest from bank} = 9000 \times 0.03 = 270 \] Let \( x \) be the amount to be invested in bonds at \( 7\% \). The interest from the bond investment will be: \[ \text{Interest from bonds} = x \times 0.07 \] The total investment will be \( 9,000 + x \), and the total interest earned from both investments must equal \( 5\% \) of that total amount: \[ \text{Total Interest} = 270 + 0.07x = 0.05(9000 + x) \] Now, we can set up an equation based on this information: \[ 270 + 0.07x = 0.05 \times (9000 + x) \] Expanding the right side: \[ 270 + 0.07x = 450 + 0.05x \] Rearranging gives: \[ 0.07x - 0.05x = 450 - 270 \] \[ 0.02x = 180 \] Now, solving for \( x \): \[ x = \frac{180}{0.02} = 9000 \] Thus, an additional \( \$ 9,000 \) needs to be invested in bonds at \( 7\% \) to achieve an overall \( 5\% \) return on the total investment.