A man has $380,000 invested in three rental properties. One property earns 7.5% per year on the investment, the second earns 7%, and the third earns 9%. The tolal annual earnings from the three properties is $30,750, 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 7%, and z represent the investment at 9%. Complete parts (a) through (d) below. x+y+z=380000 (Type an equation. Do not include the $ symbol in your answer.) b. Write an equation that states that the sum of the returns from all three investments is $30,750. 0.075x +0.07y+0.09z = 30,750 (Type an equation. Do not include the $ symbol in your answer.) c. Write an equation that states that the amount invested at 9% equals the sum of the other two investments. z=x+y (Type an equation. Do not include the $ symbol in your answer.) d. Solve the system of equations to find how much is invested in each property. O A. There is one solution. The man invested $ at 7.5%, $ at 7%, and $ at 9%. O B. There are infinitely many solutions. If the man invests $z at 9%, then he invests $ at 7.5% and $ at 7%. (Type expressions using z as the variable.)
A man has $380,000 invested in three rental properties. One property earns 7.5% per year on the investment, the second earns 7%, and the third earns 9%. The tolal annual earnings from the three properties is $30,750, 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 7%, and z represent the investment at 9%. Complete parts (a) through (d) below. x+y+z=380000 (Type an equation. Do not include the $ symbol in your answer.) b. Write an equation that states that the sum of the returns from all three investments is $30,750. 0.075x +0.07y+0.09z = 30,750 (Type an equation. Do not include the $ symbol in your answer.) c. Write an equation that states that the amount invested at 9% equals the sum of the other two investments. z=x+y (Type an equation. Do not include the $ symbol in your answer.) d. Solve the system of equations to find how much is invested in each property. O A. There is one solution. The man invested $ at 7.5%, $ at 7%, and $ at 9%. O B. There are infinitely many solutions. If the man invests $z at 9%, then he invests $ at 7.5% and $ at 7%. (Type expressions using z as the variable.)
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.7: Direct And Inverse Variation
Problem 36PS
Related questions
Question
![A man has $380,000 invested in three rental properties. One property earns 7,5% per year on the investment, the second earns 7%, and the third earns 9%. The total
annual earnings from the three properties is $30,750, 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 7%, and z represent the investment at 9%.
Complete parts (a) through (d) below.
x+y+z=380000
(Type an equation. Do not include the $ symbol in your answer.)
b. Write an equation that states that the sum of the returns from all three investments is $30,750.
0.075x+0.07y +0.09z = 30,750
(Type an equation. Do not include the $ symbol in your answer.)
c. Write an equation that states that the amount invested at 9% equals the sum 'of the other two investments.
>
z =x+y
(Type an equation. Do not include the $ symbol in your answer.)
d. Solve the system of equations to find how much is invested in each property.
O A. There is one solution. The man invested $
at 7.5%, $
at 7%, and $
at 9%.
O B. There are infinitely many solutions. If the man invests $z at 9%, then he invests $
at 7.5% and $
at 7%.
(Type expressions using z as the variable.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0775f4f-4f78-48a8-b68d-a762f326d59e%2F2ae1073f-e59f-4138-be5a-c4bdef8b5d0b%2Fh991zvd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A man has $380,000 invested in three rental properties. One property earns 7,5% per year on the investment, the second earns 7%, and the third earns 9%. The total
annual earnings from the three properties is $30,750, 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 7%, and z represent the investment at 9%.
Complete parts (a) through (d) below.
x+y+z=380000
(Type an equation. Do not include the $ symbol in your answer.)
b. Write an equation that states that the sum of the returns from all three investments is $30,750.
0.075x+0.07y +0.09z = 30,750
(Type an equation. Do not include the $ symbol in your answer.)
c. Write an equation that states that the amount invested at 9% equals the sum 'of the other two investments.
>
z =x+y
(Type an equation. Do not include the $ symbol in your answer.)
d. Solve the system of equations to find how much is invested in each property.
O A. There is one solution. The man invested $
at 7.5%, $
at 7%, and $
at 9%.
O B. There are infinitely many solutions. If the man invests $z at 9%, then he invests $
at 7.5% and $
at 7%.
(Type expressions using z as the variable.)
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