An investor invested a total of $1400 in two mutual funds. One fund earned a 6% profit while the other earned a 2% profit. If the investor's total profit was $72, how much was invested in each mutual fund?
add up the interest earned:
.06x + .02(1400-x) = 72
x = 1100
so, 1100 at 6% and 300 at 2%
To solve this problem, we can set up a system of equations:
Let x be the amount invested in the fund that earned a 6% profit.
Let y be the amount invested in the fund that earned a 2% profit.
We know that the total amount invested is $1400:
x + y = 1400 ---(equation 1)
We also know that the total profit earned is $72. Since the profit is calculated as a percentage of the investment, we can express the profit for each fund as follows:
Profit from the fund that earned a 6% profit: 0.06x
Profit from the fund that earned a 2% profit: 0.02y
The total profit earned by the investor is $72:
0.06x + 0.02y = 72 ---(equation 2)
Now we have a system of two equations that we can solve to find the values of x and y.
To solve this system of equations, we can use the substitution method or elimination method. In this case, let's use the substitution method:
From equation 1, we have:
x = 1400 - y
Substituting this value of x into equation 2, we get:
0.06*(1400 - y) + 0.02y = 72
Expanding and simplifying, we have:
84 - 0.06y + 0.02y = 72
Combining like terms, we get:
0.04y = 12
Dividing both sides by 0.04, we get:
y = 300
Substituting this value of y back into equation 1, we can solve for x:
x + 300 = 1400
x = 1400 - 300
x = 1100
Therefore, $1100 was invested in the fund that earned a 6% profit, and $300 was invested in the fund that earned a 2% profit.