Answer:
Scott invested:
$3,100 at bank 1
$2,800 at bank 2
Step-by-step explanation:
Use formula
[tex]I=P\cdot r \cdot t,[/tex]
where
I = interest,
P = principal,
t = time,
r = rate (as decimal)
Let $x be the amount of money Scott invested at bank 1, then $(5,900-x) is his investment at bank 2
Bank 1:
[tex]P_1=x\\ \\r_1=0.1\\ \\t_1=1\\ \\I_1=P_1\cdot r_1\cdot t_1=x\cdot 0.1\cdot 1=0.1x[/tex]
Bank 2:
[tex]P_2=(5,900-x)\\ \\r_2=0.061\\ \\t_2=1\\ \\I_2=P_2\cdot r_2\cdot t_2=(5,900-x)\cdot 0.06\cdot 1=0.06(5,900-x)[/tex]
Total interest = $478, then
[tex]I_1+I_2=478\\ \\0.1x+0.06(5,900-x)-478\\ \\10x+6(5,900-x)=47,800\\ \\10x+35,400-6x=47,800\\ \\10x-6x=47,800-35,400\\ \\4x=12,400\\ \\x=3,100\\ \\5,900-x=5,900-3,100=2,800[/tex]