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?
A boat travels 60 km upstream and back again in 8 hours. If the speed of the boat is 16 km/h, what is the speed of the current? Please Show Work
To solve this problem, we can use a system of linear equations.
Let's assume that Sally invested x dollars at 9% per year. Therefore, she invested (4500 - x) dollars at 6% per year.
The interest earned from the 9% investment is calculated using the formula: (x * 0.09) or 0.09x.
The interest earned from the 6% investment is calculated using the formula: ((4500 - x) * 0.06) or 0.06(4500 - x).
According to the problem, the return from the 9% investment exceeds that from the 6% investment by $180. This can be written as the following equation:
0.09x - 0.06(4500 - x) = 180
Now, let's solve this equation to find the value of x.
0.09x - 0.06(4500 - x) = 180
0.09x - 0.06 * 4500 + 0.06x = 180
0.09x - 270 + 0.06x = 180
0.15x - 270 = 180
0.15x = 450
x = 450 / 0.15
x = 3000
Therefore, Sally invested $3000 at 9% per year, and she invested $1500 at 6% per year.