A person invested 20,000$ in stocks and bonds. Her investment in bonds is 5,000$ more than half her investment in stocks. How much did she invest in stocks? how much did she invest in bonds?
b = s/2 + 5000
b+s = 20000
b=10000
s=10000
no
To find out how much the person invested in stocks and bonds, let's break down the given information into equations:
Let's assume the amount invested in stocks is "S" dollars.
So, the amount invested in bonds would be "B" dollars.
According to the information provided, the investment in bonds is $5,000 more than half of the investment in stocks.
This can be written as B = (1/2)S + $5,000.
We also know that the total investment is $20,000.
Therefore, the sum of the investments in stocks and bonds should equal $20,000. We can write this as S + B = $20,000.
Now, we have two equations:
Equation 1: B = (1/2)S + $5,000
Equation 2: S + B = $20,000
To solve these equations, we can substitute Equation 1 into Equation 2 to eliminate the variable "B."
Substituting B from Equation 1 into Equation 2, we get:
S + ((1/2)S + $5,000) = $20,000
Simplifying this equation:
(3/2)S + $5,000 = $20,000
Subtracting $5,000 from both sides:
(3/2)S = $15,000
Now, to solve for 'S,' we can multiply both sides by 2/3:
S = ($15,000) * (2/3)
S = $10,000
Hence, the person invested $10,000 in stocks.
To determine the investment in bonds, we can substitute the value of 'S' back into Equation 1:
B = (1/2) * $10,000 + $5,000
B = $5,000 + $5,000
B = $10,000
Thus, the person invested $10,000 in bonds as well.