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?
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To solve this problem, we can use a system of equations. Let's denote the amount Carlos invested at 5% as x, and the amount he invested at 6% as (10000 - x), since the total amount he invested is $10,000.
Now, let's set up the equations based on the information given. The equation for the annual income from the 5% investment is 0.05x, and the equation for the annual income from the 6% investment is 0.06(10000 - x).
We are told that the total annual income from both investments was $575, so we can set up the equation:
0.05x + 0.06(10000 - x) = 575
Let's simplify this equation:
0.05x + 600 - 0.06x = 575
Combine like terms:
-0.01x + 600 = 575
Now, let's isolate x by subtracting 600 from both sides:
-0.01x = 575 - 600
-0.01x = -25
Divide both sides by -0.01 to solve for x:
x = -25 / -0.01
x = 2500
So Carlos invested $2,500 at a 5% rate.
To find out how much he invested at a 6% rate, we can subtract $2,500 from the total investment:
10000 - x = 10000 - 2500 = $7,500
Carlos invested $7,500 at a 6% rate.
Therefore, Carlos invested $2,500 at 5% and $7,500 at 6%.