Question

Michael perez deposited a total of $2000 with two savings institutions. one pays interest at a rate of 6%/year, whereas the other pays interest at a rate of 7%/year. if michael earned a total of $136 in interest during a single year, how much did he deposit in each institution? (let x and y denote the amount of money, in dollars, invested at 6% and 7%, respectively.)

Answer 1

Amount invested at a rate of 6% =
`\$400`

Amount invested at a rate of 7% =
`\$1600`

Step-by-step explanation:

Let x and y denote the amount of money, in dollars, invested at 6% and 7%, respectively.

Total amount deposited = $2000

`x+y=2000`

`x=2000-y`

Interest earned on amount
`x` =
`(6)/(100)x`

Interest earned on amount
`y` =
`(7)/(100)y`

Total interest earned
`=(6)/(100)x+(7)/(100) y`

As Michael earned a total of $136 in interest during a single year,

`(6)/(100)x+(7)/(100) y=136\\6x+7y=13600`

Put
`x=2000-y`

`6(2000-y)+7y=13600\\12000-6y+7y=13600\\12000+y=13600\\y=13600-12000\\y=1600`

So,

`x=2000-1600=400`

Amount invested at a rate of 6% =
`\$400`

Amount invested at a rate of 7% =
`\$1600`