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?

Question

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?

Answer 1

8000=LR + HR (lower rate $, higherrate$)

.08*LR+ .10HR=700

solve for LR, HR.

Answer 2

LR 56

HR 70

Answer 3

To solve this problem, we can use the formula for simple interest: Interest = Principal * Rate * Time.

Let's assume Rosa invested x dollars at 8% interest, and (8000 - x) dollars at 10% interest.

For the first investment at 8%:

Interest1 = x * 8% * 1 year
= 0.08x

For the second investment at 10%:

Interest2 = (8000 - x) * 10% * 1 year
= 0.10(8000 - x)

Given that the total interest is $700, we can create the following equation:

0.08x + 0.10(8000 - x) = 700

Now, let's simplify and solve the equation:

0.08x + 800 - 0.10x = 700
-0.02x = -100
x = 5000

So, Rosa invested $5000 at 8% interest and the remaining $3000 (8000 - 5000) at 10% interest.