Rosa invested $8000 for one year, part ast 8% annual interest and the balance at 10% annual interest. Her total interest for the year was $700. How much money did she invest at each rate?
just add up the interest on each part. If $x was at 8%, the rest (8000-x) was at 10%. So,
.08x + .10(8000-x) = 700
To find out how much money Rosa invested at each interest rate, we can set up a system of equations.
Let's say Rosa invested x dollars at 8% interest and (8000 - x) dollars at 10% interest.
The interest earned from the amount invested at 8% is given by: 0.08x
The interest earned from the amount invested at 10% is given by: 0.10(8000 - x)
So, we have the following equation:
0.08x + 0.10(8000 - x) = 700
Now we can solve for x:
0.08x + 0.10(8000 - x) = 700
0.08x + 800 - 0.10x = 700
-0.02x = -100
x = -100 / -0.02
x = 5000
Therefore, Rosa invested $5000 at 8% interest and the remaining amount, $8000 - $5000 = $3000, at 10% interest.