dondre54
21.12.2019 •
Mathematics
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.
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Ответ:
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
Ответ:
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