I'm completely drawing a blank on how to do this.
A woman has $500,000 invested into two real estate properties. One yields an annual return on 12% and the other returns 15% per year on her investment. Her total annual return from the two investments is $64,500. If X represents 12% investment and Y represents 15% investment...
a. write an equation that states that the sum of the investments is equal to $500,000
x+y=500,000
b. What is the annual return on the 12% investment?
c. What is the annual return on the 15% investment?
d. write an equation that states the sum of the annual returns is $64,000.
12x+15y=64,500
e. solve the problem simultaneously to find how much is invested in each property.
To solve the problem simultaneously and find how much is invested in each property, we can use a method called substitution.
Let's start by solving part b of the problem, which is finding the annual return on the 12% investment.
We know that the annual return on the 12% investment is X. Therefore, the equation for the annual return on the 12% investment can be written as:
0.12X
Similarly, for part c, the annual return on the 15% investment would be:
0.15Y
Now, let's solve part d of the problem, which is writing an equation that states the sum of the annual returns is $64,500. The equation can be written as:
0.12X + 0.15Y = 64,500
Now, we have a system of two equations:
x + y = 500,000 (equation from part a)
0.12X + 0.15Y = 64,500 (equation from part d)
To solve this system, we can use the substitution method. From part a, we know that x + y = 500,000. Therefore, we can rewrite it as:
y = 500,000 - x
So, we substitute y in the second equation with (500,000 - x):
0.12x + 0.15(500,000 - x) = 64,500
Now, we can solve for x:
0.12x + 75,000 - 0.15x = 64,500
Combine like terms:
-0.03x + 75,000 = 64,500
Subtract 75,000 from both sides:
-0.03x = -10,500
Divide both sides by -0.03:
x = -10,500 / -0.03
x = 350,000
Now, substitute the value of x into the equation y = 500,000 - x:
y = 500,000 - 350,000
y = 150,000
So, the solution is x = 350,000 and y = 150,000. This means $350,000 is invested in the 12% property and $150,000 is invested in the 15% property.