A women has $500,000 invested in two rental properties. One yields an annual return of 14% on her investment, and the other returns 10% per year on her investment. Her total annual return from the two investments is $59,000. How much is invested at each return?

A + B = 500,000

.14 A + .10 B = 59,000
multiply second equation by 10

1.0 A + B = 500,000
1.4 A + B = 590,000
--------------------- subtract
-.4 A = -90,000
A = 225,000 etc

Thanks Damon!

You are welcome.

To determine how much is invested at each return, you can set up a system of equations based on the given information.

Let's say x is the amount invested in the property with a 14% return, and y is the amount invested in the property with a 10% return.

According to the problem, the total invested amount is $500,000:
x + y = $500,000 Equation 1

The annual return from the property with a 14% return is 14% of x:
0.14x

The annual return from the property with a 10% return is 10% of y:
0.10y

The total annual return from both investments is $59,000:
0.14x + 0.10y = $59,000 Equation 2

Now, you need to solve this system of equations.

One way to do this is by substitution. Solve Equation 1 for x and substitute it into Equation 2:

x = $500,000 - y

0.14($500,000 - y) + 0.10y = $59,000

Expand and simplify:

$70,000 - 0.14y + 0.10y = $59,000

Combine like terms:

$70,000 - $59,000 = 0.14y - 0.10y

$11,000 = 0.04y

Divide both sides by 0.04:

$11,000 / 0.04 = y

y = $275,000

Now substitute the value of y back into Equation 1 to find x:

x + $275,000 = $500,000

x = $500,000 - $275,000

x = $225,000

Therefore, $225,000 is invested in the property with a 14% return, and $275,000 is invested in the property with a 10% return.