An investor invested a total of $500 in two mutual funds. One fund earned a 8% profit while the other earned a 4% profit. If the investor's total profit was $32, how much was invested in each mutual fund? The amount invested in the mutual fund that earned 8% was? The amount invested in the mutual fund that earned 4% was?
if x at 8%, then 500-x at 4%
adding up the interest,
.08x + .04(500-x) = 32.00
x = 300
so,
$300 @ 8%
$200 @ 4%
To find the amounts invested in each mutual fund, we can use a system of linear equations.
Let's assume the amount invested in the mutual fund that earned a 8% profit is x dollars, and the amount invested in the mutual fund that earned a 4% profit is y dollars.
From the given information, we know that the total amount invested is $500, and the total profit is $32.
So we have two equations:
1) x + y = $500 (equation for the total amount invested)
2) 0.08x + 0.04y = $32 (equation for the total profit)
To solve this system of equations, we can use the substitution method or the elimination method. Let's use the substitution method:
From equation 1) we can rewrite it as x = $500 - y.
Now substitute this expression for x in equation 2):
0.08($500 - y) + 0.04y = $32
Simplify the equation:
40 - 0.08y + 0.04y = $32
40 - 0.04y = $32
Subtract 40 from both sides:
-0.04y = -$8
Divide by -0.04:
y = $200
Now substitute the value of y back into equation 1) to find x:
x + $200 = $500
x = $300
Therefore, the amount invested in the mutual fund that earned 8% is $300, and the amount invested in the mutual fund that earned 4% is $200.