Sally invested a total of $4500, some at 9% per year and the rest at 6% per year. The return from the 9% investment exceeds that from the 6% investment by $180. How much did she invest at each rate?
To solve this problem, let's assume Sally invested x dollars at 9% per year, and she invested (4500 - x) dollars at 6% per year.
At 9% per year, Sally would earn an annual return of 0.09x dollars.
At 6% per year, Sally would earn an annual return of 0.06(4500 - x) dollars.
According to the given information, the return from the 9% investment exceeds that from the 6% investment by $180. This can be expressed as:
0.09x - 0.06(4500 - x) = 180
Now, let's solve this equation step by step:
0.09x - 0.06(4500 - x) = 180
0.09x - 270 + 0.06x = 180 (Distribute -0.06 to (4500 - x))
Combine like terms:
0.15x - 270 = 180
Add 270 to both sides of the equation:
0.15x = 450
Divide both sides by 0.15:
x = 3000
Therefore, Sally invested $3000 at 9% per year, and she invested $1500 (4500 - 3000) at 6% per year.