Given:
Principal amount = $6000.
Let x be the amount invested at 5%.
So, 6000-x be the amount invested at 10%.
The annual interest is $590
The equation is written as,
[tex]\begin{gathered} 5\text{ \%x+(6000-x)10 \%=590} \\ \frac{5}{100}x+(6000-x)\frac{10}{100}=590 \\ 0.05x+(6000-x)0.1=590 \\ 0.05x+600-0.1x=590 \\ -0.05x=-10 \\ x=\frac{10}{0.05} \\ x=200 \\ 6000-x=6000-200=5800 \end{gathered}[/tex]
Answer: At 5%, the amount invested is $200, and at 10%, the amount invested is $5800.
