Answer:
The amount invested at 4% was $600
The amount invested at 7.5% was $3,600
Step-by-step explanation:
Let
x ----> the amount invested at 4%
$4,200-x -----> amount invested at 7.5%
we know that
The total interest earned is equal to the interest earned by the amount invested at 4% plus the interest earned by the amount invested at 7.5%
Remember that
[tex]4\%=4/100=0.04[/tex]
[tex]7.5\%=7.5/100=0.075[/tex]
[tex]7\%=7/100=0.07[/tex]
so
The linear equation that represent this situation is
[tex]0.04x+0.075(4,200-x)=0.07(4,200)[/tex]
Solve for x
[tex]0.04x+315-0.075x=294[/tex]
[tex]0.075x-0.04x=315-294[/tex]
[tex]0.035x=21[/tex]
[tex]x=\$600[/tex]
[tex]\$4,200-x=\$3,600[/tex]
therefore
The amount invested at 4% was $600
The amount invested at 7.5% was $3,600