$50,000 was invested in bonds at %6and stocks at 8%. how much money was invested in each if the total return was $32,000?
If $x is at 6%, then the rest (50000-x) is at 8%. So, just add up the interest:
.06x + .08(50000-x) = 32000
Now just solve for x.
466.67
To solve this problem, we can use the concept of a system of equations. Let's assume that the amount of money invested in bonds is x dollars, and the amount of money invested in stocks is y dollars.
According to the problem, the total amount invested is $50,000:
x + y = 50000 -- Equation 1
The total return from both investments is $32,000. The return from the bond investment can be calculated by multiplying the amount invested in bonds (x) by the interest rate (6% or 0.06), and the return from the stock investment is calculated by multiplying the amount invested in stocks (y) by the interest rate (8% or 0.08):
0.06x + 0.08y = 32000 -- Equation 2
Now we have a system of two equations (Equation 1 and Equation 2) that we can solve simultaneously to find the values of x and y.
One way to solve this system is by substitution. We can solve Equation 1 for x in terms of y and substitute it into Equation 2. Let's solve Equation 1 for x:
x = 50000 - y
Substituting x into Equation 2:
0.06(50000 - y) + 0.08y = 32000
Now we can simplify and solve for y:
3000 - 0.06y + 0.08y = 32000
0.02y = 2000
y = 2000 / 0.02
y = 100,000
So, $100,000 was invested in stocks.
To find the amount invested in bonds, substitute the value of y back into Equation 1:
x + 100,000 = 50,000
x = 50,000 - 100,000
x = -50,000
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