Let \( x \) be the amount of money Nico invests at 6%. Then, the amount he invests at 4% would be \( x - 900 \).
The interest earned from the 6% investment in one year is:
\[ 0.06x \]
The interest earned from the 4% investment in one year is:
\[ 0.04(x - 900) \]
According to the problem, the total interest from both investments is $154. Therefore, we can set up the following equation:
\[ 0.06x + 0.04(x - 900) = 154 \]
Now, let's distribute and simplify the equation:
\[ 0.06x + 0.04x - 0.04 \times 900 = 154 \]
Calculating \( 0.04 \times 900 \):
\[ 0.04 \times 900 = 36 \]
So, the equation becomes:
\[ 0.06x + 0.04x - 36 = 154 \]
Combining like terms:
\[ 0.1x - 36 = 154 \]
Next, add 36 to both sides of the equation:
\[ 0.1x = 154 + 36 \]
\[ 0.1x = 190 \]
Now divide by 0.1:
\[ x = \frac{190}{0.1} = 1900 \]
So, Nico invests \( x = 1900 \) at 6%. Now we will find the amount he invests at 4%:
\[ x - 900 = 1900 - 900 = 1000 \]
Thus, Nico invests:
- $1900 at 6%
- $1000 at 4%
To verify, we can calculate the interest from both investments:
Interest from 6% investment:
\[ 0.06 \times 1900 = 114 \]
Interest from 4% investment:
\[ 0.04 \times 1000 = 40 \]
Total interest:
\[ 114 + 40 = 154 \]
The calculations check out, confirming the amounts invested:
- $1900 at 6%
- $1000 at 4%