Carlos invested $10,000. part ot 5% and the rest at 6%. His total annual income from these investments was $575. How nuch did he invest at each rate?

The subject is math, not 10th grade.

575=.05(X)+ .06(10,000-x)

solve for x

To solve this problem, we can set up a system of equations.

Let's say Carlos invested x dollars at 5% interest, and the rest of the amount (10000 - x) dollars at 6% interest.

The equation for the income from the investment at 5% interest is:
0.05x

And the equation for the income from the investment at 6% interest is:
0.06(10000 - x)

We know that the total annual income from the investments is $575, so we can set up the equation:
0.05x + 0.06(10000 - x) = 575

Now we can solve this equation to find the value of x.

0.05x + 0.06(10000 - x) = 575
0.05x + 600 - 0.06x = 575
-0.01x = -25
x = -25 / -0.01
x = 2500

So Carlos invested $2500 at 5% interest, and the remaining amount he invested at 6% interest would be:
10000 - 2500 = 7500

Therefore, Carlos invested $2500 at 5% and $7500 at 6%.