Answer:
Investor invested $7,800 at 8% and $6,200 at 6.5%
Step-by-step explanation:
Use formula
[tex]I=P\cdot r\cdot t,[/tex]
where
I = interest
P = principal
r = rate (as decimal)
t = time
First investment:
[tex]P_1=x\\ \\r_1=0.08\\ \\t_1=1[/tex]
then
[tex]I_1=x\cdot 0.08\cdot 1\\ \\I_1=0.08x[/tex]
Second investment:
[tex]P_2=14,000-x\\ \\r_2=0.065\\ \\t_2=1[/tex]
then
[tex]I_2=(14,000-x)\cdot 0.065\cdot 1\\ \\I_2=0.065(14,000-x)[/tex]
The amount of interest earned for 1 year was $1,027, then
[tex]I_1+I_2=1,027\\ \\0.08x+0.065(14,000-x)=1,027\\ \\0.08x+910-0.065x=1,027\\ \\0.08x-0.065x=1,027-910\\ \\0.015x=117\\ \\x=7,800\\ \\14,000-x=6,200[/tex]
Investor invested $7,800 at 8% and $6,200 at 6.5%
