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

Answer:

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

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

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 $x$ = $\frac{6}{100}x$

Interest earned on amount $y$ = $\frac{7}{100}y$

Total interest earned $=\frac{6}{100}x+\frac{7}{100} y$

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

$\frac{6}{100}x+\frac{7}{100} y=136\\6x+7y=13600$

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% = $\ 1600$