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.
b) .12x
c).15y
d) your equation should say
.12x + .15y = 64500
times 100
12x + 15y = 6450000
divide it by 3
4x + 5y = 2150000
first equation times 4
4x + 4y = 2000000
subtract them:
y = 150,000
then x = 350,000
check:
.12(350000) + .15(150000) = 64500
To solve this problem simultaneously, we will use a method called "substitution" or "elimination." Let's start.
Since we are given that X represents the 12% investment and Y represents the 15% investment, we can use these variables in our equations.
a. The equation that states the sum of the investments is equal to $500,000 is:
x + y = 500,000
b. To find the annual return on the 12% investment, we can use the formula:
Annual return on 12% investment = 12% of the investment amount
Which can be written as:
Annual return on 12% investment = 0.12x
c. Similarly, the annual return on the 15% investment can be found using:
Annual return on 15% investment = 15% of the investment amount
So, we have:
Annual return on 15% investment = 0.15y
d. The equation that states the sum of the annual returns is $64,500 is given as:
12x + 15y = 64,500
Now, to solve the problem simultaneously, we can use the substitution method or the elimination method. Let's use the substitution method here.
We can rearrange the first equation x + y = 500,000 to solve for x:
x = 500,000 - y
Now, substitute this value of x in the second equation:
12(500,000 - y) + 15y = 64,500
Simplify the equation:
6,000,000 - 12y + 15y = 64,500
6,000,000 + 3y = 64,500
3y = 64,500 - 6,000,000
3y = -5,935,500
y = -5,935,500 / 3
y ≈ -1,978,500
Since it doesn't make sense to have a negative investment, it seems there might be an error in the problem statement or calculations. Please check the given values or calculations provided.