Respuesta :
SOLUTION
Let the money(principal) invested at 9% be x and
Let the money(principal) invested at 8% be y
Using the simple interest formula
[tex]I=\frac{PRT}{100}[/tex]We have
[tex]\begin{gathered} I_x\text{ that is interest at principal x becomes } \\ I_x=\frac{x\times9\times1}{100} \\ I_x=0.09x \end{gathered}[/tex]And
[tex]\begin{gathered} I_y\text{ that is interest at principal y becomes } \\ I_y=\frac{y\times8\times1}{100} \\ I_y=0.08y \\ \text{But y = 200,000 - }x \\ \text{Hence } \\ I_y=0.08(\text{200,000 - }x) \\ I_y=16000-0.08x \end{gathered}[/tex]Combining, we have
[tex]\begin{gathered} 0.09x+16000-0.08x=17,200 \\ 0.09x-0.08x=17,200-16,000 \\ 0.01x=1200 \\ x=\frac{1200}{0.01} \\ x=120,000\text{ dollars } \end{gathered}[/tex]Then,
[tex]\begin{gathered} y=200,000-x \\ y=200,000-120,000 \\ y=80,000\text{ dollars } \end{gathered}[/tex]Hence, the answer is 9% interest rate was $120,000 and 8% interest rate was $80,000
