an investor invested a total of $3,100 in two mutual funds. One fund earned a 8% profit where the other earned 5% profit. If the investor's total profit was $209, how much was invested in each mutual fund?
To solve this problem, we can set up a system of equations.
Let's assume the amount invested in the mutual fund that earned an 8% profit is 'x', and the amount invested in the mutual fund that earned a 5% profit is 'y'.
We are given two pieces of information:
1. The total amount invested in the mutual funds is $3,100: x + y = 3100.
2. The total profit earned is $209: 0.08x + 0.05y = 209.
Now we can solve this system of equations using substitution or elimination.
Let's solve by substitution:
From equation 1, we have x = 3100 - y.
Now substitute this value for x in equation 2 and solve for y:
0.08(3100 - y) + 0.05y = 209.
Simplify the equation:
248 - 0.08y + 0.05y = 209.
Combine like terms:
0.03y = 209 - 248.
0.03y = -39.
Divide both sides by 0.03:
y = -39 / 0.03.
y = -1300.
This implies that the investor invested -$1,300 in the mutual fund that earned a 5% profit. However, an investment cannot be negative.
Here, we realize that there must be an error in the problem because the solution leads to a negative investment, which is not possible. Please double-check the given information or the conditions of the problem.