Answer:
The amount invested at 4.5% was [tex]\$3,000[/tex]
The amount invested at 5% was [tex]\$6,000[/tex]
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
Let
x -----> the amount invested at 4.5%
9,000-x -----> the amount invested at 5%
in this problem we have
[tex]t=1\ year\\ P1=\$x\\ P2=\$(9,000-x)\\I=\$435\\r1=0.045\\r2=0.05[/tex]
substitute
[tex]435=x(0.045*1)+(9,000-x)(0.05*1)[/tex]
[tex]435=0.045x+450-0.05x[/tex]
[tex]0.05x-0.045x=450-435[/tex]
[tex]0.005x=15[/tex]
[tex]x=\$3,000[/tex]
so
[tex]9,000-x=\$6,000[/tex]
therefore
The amount invested at 4.5% was [tex]\$3,000[/tex]
The amount invested at 5% was [tex]\$6,000[/tex]
