A total of 8000 dollars is invested in two funds paying 4 percent and 5 percent annual interest,. The combined interest for the year is 350 dollars. How much of the 8000 dollars is invested in each fund?
funds:
8000=F1 + F2 where f1 and f2 are each of the twofunds.
income;
F1*.04+F2*.05=350
then you solve either F2, or F1 by substution, then go back and solve the other.
To solve this problem, we can use a system of equations.
Let's assume that the amount invested in the fund paying 4 percent interest is x dollars.
Therefore, the amount invested in the fund paying 5 percent interest will be (8000 - x) dollars, as the total investment is $8000.
Now, we can set up two equations based on the given information:
Equation 1: (x * 0.04) + ((8000 - x) * 0.05) = 350
This equation represents the combined interest earned from both funds, which should be equal to $350.
Equation 2: x + (8000 - x) = 8000
This equation represents the total investment, which should be equal to $8000.
Now, we can solve this system of equations to find the value of x and (8000 - x).
From Equation 2, we can simplify it to:
x + 8000 - x = 8000
8000 = 8000
This equation is always true, so it doesn't provide any useful information for finding the values of x and (8000 - x).
Now, let's solve Equation 1:
0.04x + 0.05(8000 - x) = 350
0.04x + 400 - 0.05x = 350
-0.01x = 350 - 400
-0.01x = -50
x = -50 / -0.01
x = 5000
Therefore, $5000 is invested in the fund paying 4 percent interest, and $3000 (8000 - 5000) is invested in the fund paying 5 percent interest.