Aman has s400,000 invested in three rental properties. one property earns 7.5% per year on the investment, the second earns 8%, and the third earns 9%. the total annual earnings from the three properties is s33,700, and the amount invested at 9% equals the sum of the first two investments. let x equal the investment at 7.5%, y equal the investment at 8%, and z represent the investment at 9%. a. write an equation that represents the sum of the three investments. b. write an equation that states that the sum of the returns from all three investments is $33,700. c. write an equation that states that the amount invested at 9% equals the sum of the other two investments. d. solve the system of equations to find how much is invested in each property.

the amount of money invested in the first property is $140000

the amount of money invested in the second is property is $62353

the amount of money invested in the third is property is $20235

Step-by-step explanation:

Let x represent the amount of money invested in the first property.

Let y represent the amount of money invested in the second property.

Let z represent the amount of money invested in the third property.

The man has S400,000 invested in three rental properties. This means that

x + y + z = 400000 - - - - - - - - -1

The first property earns 7.5% per year on the investment, the second earns 8%, and the third earns 9%. The total annual earnings from the three properties is S33,700. This means that

7.5/100 × x + 8/100×y + 9/100×z = 33700

0.075x + 0.08y + 0.09z = 33700 - - - - - 2

The amount invested at 9% equals the sum of the first two investments. This means that

z = x + y - - - - - - - - - - -3

Substituting equation 3 into equation 1 and equation 2, it becomes

x + y + x + y = 400000

2x + 2y = 400000 - - - - - - - - 4

0.075x + 0.08y + 0.09(x + y) = 33700

0.075x + 0.08y + 0.09x + 0.09y = 33700

0.165x + 0.17y = 33700 - - - - - - - - 5

Multiplying equation 4 by 0.165 and equation by 2, it becomes

0.33x + 0.33y = 66000

0.33x + 0.34y = 67400

Subtracting

- 0.01x= - 1400

x = $140000

Substituting x = 140000 into equation 5, it becomes

0. 165(140000) + 0.17y = 33700

23100 + 0.17y = 33700

0.17y = 33700 - 23100 = 10600

y = 10600/0.17 = $62353

z = x + y = 140000 + 62353 = $202353