Question

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

Answer 1

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

`182-0.028y+0.18y=410`

then we sum like terms

`0.152y=410-182`
`0.152y=228`

then we isolate the y

`y=(228)/(0.152)`
`y=1500`

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

`x=6500-1500`
`x=5000`

5000 amount invested at 2.8%

1500 amount invested at 18%