You have $6000 to invest in two stock funds. The first fund pays 5% annual interest and the second account pays 9% annual interest. If after a year you have made $380 in interest, how much money did you invest in each account?

I = P*r1*t+P*r2*t = $380.

I = P1*.05*1+P2*.09*1 = 380
0.05P1 + 0.09P2 = 380.

Multiply both sides by 100:
Eq1: 5P1 + 9P2 = 38000.
Eq2: P1 + P2 = 6000.
Multiply Eq2 by -5:
5P1 + 9P2 = 38000
-5P1 + -5P2 = -30000
Add the 2 Eqs and

I = P*r1*t+P*r2*t = $380.

I = P1*.05*1+P2*.09*1 = 380
0.05P1 + 0.09P2 = 380.

Multiply both sides by 100:
Eq1: 5P1 + 9P2 = 38000.
Eq2: P1 + P2 = 6000.
Multiply Eq2 by -5:
5P1 + 9P2 = 38000
-5P1 + -5P2 = -30000
Add the 2 Eqs:
4P2 = 8000
P2 = $2000 = Investment @ 9%.

In Eq2, substitute 2000 for P2:
P1 + 2000 = 6000
P1 = $4000 = Investment @ 5%.

thank you so much

To solve this problem, let's set up the equations based on the given information.

Let's assume that the amount of money invested in the first fund is "x" dollars, and the amount of money invested in the second fund is "y" dollars.

According to the problem, the first fund pays 5% annual interest, which can be expressed as 0.05x, and the second fund pays 9% annual interest, which can be expressed as 0.09y.

The total interest earned after a year is $380.

Now we can write the equation based on the total interest:

0.05x + 0.09y = $380 ...(Equation 1)

We also know that the total amount invested is $6000:

x + y = $6000 ...(Equation 2)

Now we have a system of two equations with two variables. We can solve this system of equations using various methods such as substitution or elimination. Let's solve it using the substitution method:

From Equation 2, let's solve for x:

x = $6000 - y

Substitute this expression for x in Equation 1:

0.05($6000 - y) + 0.09y = $380

Expand and simplify:

300 - 0.05y + 0.09y = $380

0.04y = $80

Divide both sides by 0.04:

y = $80 / 0.04 = $2000

Now substitute the value of y into Equation 2 to find the value of x:

x + $2000 = $6000

x = $6000 - $2000 = $4000

Therefore, you invested $4000 in the first fund that pays 5% annual interest and $2000 in the second fund that pays 9% annual interest.