Reggie invests $12,000, part at 7% annual interest and part at 8.5% annual interest. how much is invested at each rate if reggie's total annual interest is $900?

Let us say that:

x = invested at 7%

y = invested at 8.5%

and that:

x + y = 12,000

We can also say that:

0.07 x + 0.085 y = 900

Therefore:

0.07 x + 0.085 (12000 - x) = 900

0.07 x + 1020 - 0.085 x = 900

- 0.015 x = - 120

x = $8000

so y is:

y = 12000 - 8000

y = $4,000

$8000 is invested at 7% annual interest while $4000 is invested at 8.5%