Nico is saving money for his college education. He invests some money at 5%, and $2300 less than that amount at 3%. The investments produced a total of $163 interest in one year. How much did he invest at each rate?
To solve this problem, let's break it down step by step:
Let's assume that Nico invested x dollars at 5% interest. According to the problem, he also invested $2300 less than that amount at 3% interest.
So, the amount invested at 3% interest would be (x - $2300).
Now, let's calculate the interest earned from each investment:
The interest earned from the investment at 5% interest would be: (x * 5%) = 0.05x.
The interest earned from the investment at 3% interest would be: ((x - $2300) * 3%) = 0.03(x - $2300).
According to the problem, the total interest earned from both investments is $163. Therefore, we can set up the following equation:
0.05x + 0.03(x - $2300) = $163.
Simplifying the equation, we get:
0.05x + 0.03x - $69 = $163.
Combine like terms, we have:
0.08x = $163 + $69.
0.08x = $232.
Next, we can solve for x by dividing both sides of the equation by 0.08:
x = $232 / 0.08.
Calculating this, we find:
x = $2900.
So, Nico invested $2900 at 5% interest.
To find out the amount Nico invested at 3% interest, we subtract $2300 from $2900:
$2900 - $2300 = $600.
Therefore, Nico invested $600 at 3% interest.
In summary, Nico invested $2900 at 5% interest and $600 at 3% interest.