A man has $420,000 invested in three rental properties. One property earns 6.5% per year on the investment, the second earns 9%, and the third earns 8%. The total annual earnings from the three properties is $34,450, and the amount invested at 8% equals the sum of the first two investments.
A man has $420,000 invested in three rental properties. One property earns 6.5% per year on the investment, the second earns 9%, and the third earns 8%. The total annual earnings from the three properties is $34,450, and the amount invested at 8% equals the sum of the first two investments.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.3: Rules For Addition
Problem 8P
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A man has
$420,000
invested in three rental properties. One property earns
6.5%
per year on the investment, the second earns
9%,
and the third earns
8%.
The total annual earnings from the three properties is
$34,450,
and the amount invested at
8%
equals the sum of the first two investments. Let x equal the investment at
6.5%,
y equal the investment at
9%,
and z represent the investment at
8%.
Complete parts (a) through (d) below.
a. Write an equation that represents the sum of the three investments.
nothing
(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
$34,450.
nothing
(Type an equation. Do not include the $ symbol in your answer.)
c. Write an equation that states that the amount invested at
8%
equals the sum of the other two investments.nothing
(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.
There is one solution. The man invested
$nothing
at
6.5%,
$nothing
at
9%,
and
$nothing
at
8%.
There are infinitely many solutions. If the man invests $z at
8%,
then he invests
$nothing
at
6.5%
and
$nothing
at
9%.
(Type expressions using z as the variable.)
There is no solution.
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