A total of $8000 is invested: part at 5% and the remainder at 13%. How much is invested at each rate if the annual interest is $730?

$3875 at 5%

$4125 at 13%

Step-by-step explanation:

Let x = amount invested at 5%.

Let y = amount invested at 13%.

x + y = 8000

0.05x + 0.13y = 730

Solve the first equation for x and sustitute into the second one to solve by the substitution method.

x = 8000 - y

0.05(8000 - y) + 0.13y = 730

400 - 0.05y + 0.13y = 730

0.08y = 330

y = 4125

x = 8000 - 4125

x = 3875

$3875 at 5%

$4125 at 13%