A woman has a total of $9000 to invest. She invests part of the money in an account that pays 7% per year and the rest in an account that pays 8% per year. If the interest earned in the first year is $664, how much did she invest in each account?

Question

A woman has a total of $9000 to invest. She invests part of the money in an account that pays 7% per year and the rest in an account that pays 8% per year. If the interest earned in the first year is $664, how much did she invest in each account?

Answer 1

Let x = the amount invested in the 7% account

Let (9000 - x) = the amount invested in the 8% account

0.07x + 0.08(9000 - x) = 664

0.07x + 720 - 0.08x = 664

0.15x = 664 - 720

x = -56

Since x cannot be negative, the woman invested $0 in the 7% account and $9000 in the 8% account.

Answer 2

To solve this problem, we can use a system of equations.

Let's assume the woman invests x dollars in the account that pays 7% per year. Therefore, she invests (9000 - x) dollars in the account that pays 8% per year.

The interest earned in the first year from the 7% account is 0.07x.
The interest earned in the first year from the 8% account is 0.08(9000 - x).

According to the problem, the total interest earned in the first year is $664. So, we can set up the equation:

0.07x + 0.08(9000 - x) = 664

Now, let's solve for x:

0.07x + 0.08(9000 - x) = 664
0.07x + 720 - 0.08x = 664
0.07x - 0.08x = 664 - 720
-0.01x = -56
x = (-56) / (-0.01)
x = 5600

Therefore, the woman invested $5600 in the account that pays 7% per year.

To find how much she invested in the account that pays 8% per year, we subtract the amount she invested in the 7% account from the total:

9000 - 5600 = 3400

So, she invested $3400 in the account that pays 8% per year.

Therefore, the woman invested $5600 in the 7% account and $3400 in the 8% account.

Answer 3

Let's assume the amount invested at 7% per year is x dollars.

Since the total amount invested is $9000, the amount invested at 8% per year would be (9000 - x) dollars.

Using the formula for simple interest:
Interest = Principal × Rate × Time

The interest earned from the account that pays 7% per year is given as $664. Therefore, we have:

664 = x × 0.07

Solving for x, we find:

x = 664 / 0.07

x ≈ $9485.71

So, the woman invested approximately $9485.71 at 7% per year.

To find the amount invested at 8% per year, we subtract the above amount from the total investment:

9000 - 9485.71 ≈ $-485.71

Since it is not possible to have a negative investment amount, this means that there was an error in the calculations or the given information. Please double-check the problem statement and try again.