Let:
P1 = Investment #1
P2 = Investment #2
r1 = Rate #1
r2 = Rate #2
I1 = Income 1
I2 = Income 2
The 2 investment produce an annual income of $3000, so:
[tex]I1+I2=3000[/tex]One investment yields 9% per year, while the other yields 6% per year:
[tex]\begin{gathered} I1=P1\cdot r1\cdot t_{\text{ }}(1) \\ I2=P2\cdot r2\cdot t_{\text{ }}(2) \\ where\colon \\ t=1 \\ r1=0.09 \\ r2=0.06 \\ I1=0.09P1_{\text{ }}(1) \\ I2=0.06P2_{\text{ }}(2) \end{gathered}[/tex]Two Investments totaling $47,500 so:
[tex]P1+P2=47500_{\text{ }}(3)[/tex]Add (1) and (2):
[tex]\begin{gathered} I1+I2=0.09P1+0.06P2 \\ so\colon \\ 0.09P1+0.06P2=3000_{\text{ }}(4) \end{gathered}[/tex]From (4) solve for P1:
[tex]P1=\frac{3000-0.06P2}{0.09}_{\text{ }}(5)[/tex]Replace (5) into (3):
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