Answer:
the amount of money invested at the rate of 7% is $400
the amount of money invested at the rate of 8%. Is $5600
Step-by-step explanation:
Let x represent the amount of money invested at the rate of 7%.
Let y represent the amount of money invested at the rate of 8%.
The total amount of money that Brian invested is $6000. This means that
x + y = 6000
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time
Considering the investment at the rate at 7%,
P = x
R = 7%
T = 1
I = (x × 7 × 1)/100 = 0.07x
Considering the investment at the rate of 8%,
P = y
R = 8
T = 1
I = (y × 8 × 1)/100 = 0.08y
If his net annual receipts were $420, it means that
0.08y - 0.07x = 420 - - - - - - - - -1
Substituting x = 6000 - y into equation 1, it becomes
0.08y - 0.07(6000 - y) = 420
0.08y - 420 + 0.07y = 420
0.08y + 0.07y = 420 + 420
0.15y = 840
y = 840/0.15 = 5600
x = 6000 - y = 6000 - 5600
x = 400
