Question

On two investments totaling $6,000, Brian lost 7% on one and earned 8% on the other. If his net annual receipts were $420, how much was each investment?

Answer 1

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