Suppose that you have received an unexpected inheritance of $36,000. You have decided to invest the money by placing some of the money in stocks and some in bonds. To diversify, you decided that five times the amount in bonds should equal three times the amount invested in stocks. How much should be invested in stocks? Bonds?
Need to know how to set it up!! Hellp
Let B be the amount in stocks and S be the amount in bonds. Do the algebra.
5 B = 3 S
B + S = 36,000
5B + 5S = 180,000
Substitute 3S for 5B
8S = 180,000
S = 22,500
B = 36,000 - S = 13,500
To solve this problem, let's assume the amount invested in stocks as 'x' dollars.
Since "five times the amount in bonds should equal three times the amount invested in stocks," the amount invested in bonds would be 5x.
Now, to find the total amount to invest, we add the investments in stocks and bonds together:
x + 5x = $36,000
This equation can be simplified:
6x = $36,000
To solve for x, divide both sides of the equation by 6:
x = $6,000
Therefore, $6,000 should be invested in stocks, and 5 times that amount should be invested in bonds:
5x = 5 * $6,000 = $30,000
$6,000 should be invested in stocks, and $30,000 should be invested in bonds.
To solve this problem, let's break it down step by step:
Step 1: Define the variables
Let's denote the amount to be invested in stocks as "x" and the amount to be invested in bonds as "y."
Step 2: Set up the equations
Based on the given information, we know that five times the amount invested in bonds should equal three times the amount invested in stocks. So we can set up the equation:
5y = 3x
Step 3: Define the total amount to be invested
The total amount to be invested is $36,000. Therefore, we can create another equation:
x + y = 36,000
Step 4: Solve the system of equations
Now we have a system of two equations with two variables. We can solve this system using any algebraic method, such as substitution or elimination.
Let's use substitution:
In equation 1, we solve for x:
5y = 3x
x = (5/3)y
Now we substitute this value of x into equation 2:
(5/3)y + y = 36,000
(8/3)y = 36,000
Multiply both sides by (3/8):
y = 36,000 * (3/8)
y = $13,500
Step 5: Find the value of x
Now that we know the value of y, we can substitute it back into one of the original equations to solve for x. Using equation 2:
x + 13,500 = 36,000
x = 36,000 - 13,500
x = $22,500
Therefore, $22,500 should be invested in stocks and $13,500 should be invested in bonds to diversify the inheritance of $36,000.