Question

A man 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.

Answer 1

Answer: 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

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