Answer
The investment for type 1 account is 28000 dollars, the investment for type 2 account is 8000 dollars, and the investment for type 3 account is 14000 dollars,
Work Step by Step
Step 1. Identify the quantities given in the Exercise: total investment $P=50000$ dollars, interest rate of type 1 account $r_1=3\%$, interest rate of type 2 account $r_2=5.5\%$, and interest rate of type 3 account $r_3=9\%$, amount to be invested in type 1 is twice of that of type 3 $P_1=2P_3$, total targeted interests $I=2540$
Step 2: Establish equations based on the information given: Interest to be gained with type 1 account: $I_1=P_1r_1=0.03\times2P_3=0.06P_3$, Interest to be gained with type 2 account: $I_2=P_2r_2=0.055(50000-P_1-P_3)=0.055(50000-3P_3)$, Interest to be gained with type 3 account: $I_3=P_3r_3=0.09P_3$,
Step 3. The total interests equals to the sum of the above individual interests, so we have $I_1+I_2+I_3=I$ and $0.06P_3+0.055(50000-3P_3)+0.09P_3=2540$
Step 4. Solve the above equation by combining like terms to get $0.015P_3=210$, thus $P_3=14000$ dollars, $P_1=28000$ dollars, and $P_2=50000-3\times14000=8000$ dollars.
Step 5. We conclude that the investment for type 1 account is 28000 dollars, the investment for type 2 account is 8000 dollars, and the investment for type 3 account is 14000 dollars,
