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A person plans to invest a total of $6500 in one bank account at 2.8% annual interest and another bank account at 18% annual interest. how much should he invest in each account so that the total interest in one year will be $410

Respuesta :

We will do a system of equations

x amount invested at 2.8%

y amount invested at 18%

the first equation will be the total invest

x+y=6500

then the second equation is about the simple interest

0.028x+0.18y=410

then we isolate the x of the first equation

x=6500-y

we substitute this equation on the second equation

0.028(6500-y)+0.18y=410

then we simplify the expression

[tex]182-0.028y+0.18y=410[/tex]

then we sum like terms

[tex]0.152y=410-182[/tex][tex]0.152y=228[/tex]

then we isolate the y

[tex]y=\frac{228}{0.152}[/tex][tex]y=1500[/tex]

then we substitute the value of y in the equations with x isolate

[tex]x=6500-1500[/tex][tex]x=5000[/tex]

5000 amount invested at 2.8%

1500 amount invested at 18%