Solve the Problem by Writing and Solving a Suitable System $\$ 25,000$

Solve the problem by writing and solving a suitable system of equations.
-Linda invests $\$ 25,000$ for one year. Part is invested at $5 \%$ , another part at $6 \%$ , and the rest at $8 \%$ . The total income from all 3 investments is $\$ 1600$ . The income from the $5 \%$ and $6 \%$ investments is the same as the income from the $8 \%$ investment. Find the amount invested at each rate.

A) $\$ 10,000$ at $5 \%, \$ 5000$ at $6 \%, \$ 10,000$ at $8 \%$
B) $\$ 10,000$ at $5 \%, \$ 10,000$ at $6 \%, \$ 5000$ at $8 \%$
C) $\$ 8000$ at $5 \%, \$ 10,000$ at $6 \%, \$ 7000$ at $8 \%$
D) $\$ 5000$ at $5 \%, \$ 10,000$ at $6 \%, \$ 10,000$ at $8 \%$