You have two equations in two unknowns to solve.
x + y = 8000
.04x + .05y = 350
solve for x and y then continue : )
What amount should be invested in the 4 percent account?
What amount should be invested in the 5 percent account?
x + y = 8000
.04x + .05y = 350
solve for x and y then continue : )
$(8000-Po) invested at 5%
Po*0.04*1 + (8000-Po)*0.05*1 = 350.
0.04Po + 400 - 0.05Po = 350,
Po = $5000.
8000-Po = 8000-5000 = $3000.
According to the problem, the total amount invested is $8000. Therefore, the amount invested in the 5 percent account can be represented as (8000 - x) dollars.
Now, we know that the interest obtained from the 4 percent account is 4% of "x" dollars, and the interest obtained from the 5 percent account is 5% of (8000 - x) dollars.
The combined interest for the year is $350. So, we can set up the following equation:
0.04x + 0.05(8000 - x) = 350
Simplifying the equation,
0.04x + 400 - 0.05x = 350
Combining like terms,
-0.01x + 400 = 350
Subtracting 400 from both sides,
-0.01x = -50
Dividing by -0.01,
x = 5000
Therefore, $5000 should be invested in the 4 percent account.
To find the amount that should be invested in the 5 percent account, we subtract the amount invested in the 4 percent account from the total amount, which gives:
8000 - 5000 = 3000
Therefore, $3000 should be invested in the 5 percent account.
Let's assume the amount invested in the 4 percent account is 'x' dollars.
Then, the amount invested in the 5 percent account would be '8000 - x' dollars (as the total invested amount is $8000).
Now, we can set up the equations:
Equation 1: (4 percent interest)
The interest earned from the 4 percent account would be: x * 0.04
Equation 2: (5 percent interest)
The interest earned from the 5 percent account would be: (8000 - x) * 0.05
We know from the problem statement that the total interest earned is $350. So, we can set up the equation:
Equation 3: (total interest)
x * 0.04 + (8000 - x) * 0.05 = 350
Now, we can solve this system of equations to find the values of 'x' and '8000 - x'.
Step 1: Simplify equation 3:
0.04x + 0.05(8000 - x) = 350
0.04x + 400 - 0.05x = 350
-0.01x = -50
x = (-50) / (-0.01)
x = 5000
Therefore, the amount that should be invested in the 4 percent account (part I) is $5000.
To find the amount to be invested in the 5 percent account (part II), subtract the amount invested in the 4 percent account from the total investment:
8000 - 5000 = 3000
Therefore, the amount that should be invested in the 5 percent account (part II) is $3000.