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A total of ​$5900 is​ invested, part at 11​% simple interest and part at 6​%. If the total annual return from the two investments is ​$nbsp 509.00​, how much is invested at each​ rate?

Respuesta :

$ 3100 is invested at 11 % interest and $ 2800 is invested at 6 % interest

Solution:

Let x = the amount invested at 11%

Then, 5900 - x = the amount invested at 6%

The total annual return from the two investments is ​$ 509.00

Therefore,

11 % of x + 6 % of 5900 - x = 509

[tex]\frac{11}{100} \times x + \frac{6}{100} \times (5900 - x) = 509\\\\Simplify\\\\0.11x + 0.06(5900 - x) = 509\\\\0.11x + 354 - 0.06x = 509\\\\0.05x = 509 - 354\\\\0.05x = 155\\\\Divide\ both\ sides\ by\ 0.05\\\\x = 3100[/tex]

Thus, $ 3100 is invested at 11 % interest

5900 - x = 5900 - 3100 = 2800

Thus, $ 2800 is invested at 6 % interest

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