To determine the investment at each rate:
A total of $7000 is invested:
part x at 6% and the remainder 7000-x at 10%. How much is invested at each rate if the annual interest is $520
6% = 6/100 = 0.06
10% = 10/100 = 0.1
[tex]\begin{gathered} 0.06x+0.1(7000-x)=520 \\ 0.06x+700-0.1x=520 \\ 0.06x-0.1x=520-700 \end{gathered}[/tex][tex]\begin{gathered} -0.04x=-180 \\ \text{divide both side by -0.04} \\ x=-\frac{180}{-0.04} \\ x=4500 \\ x=\text{ \$4500} \end{gathered}[/tex]
x = $4500 -> invested at each 6% rate
while
7000 - x = 7000 - 4500 = $2500 ->invested at each 10% rate
Therefore the invested at each 6% rate = $4500 and invested at each 10% rate = $2500
