An investor invested a total of $2,000 in two mutual funds. One fund earned a 7% profit while the other earned a 2% profit. If the investor's total profit was $120, how much was invested in each mutual fund?
The amount invested in the mutual fund that earned 7% was $___.
The amount invested in the mutual fund that earned 2% was $___.
Let x be the amount invested in the mutual fund that earned 7%, and y be the amount invested in the mutual fund that earned 2%. Then we have:
x + y = 2000 (the total amount invested is $2,000)
0.07x + 0.02y = 120 (the total profit is $120)
To solve for x and y, we can use the first equation to solve for y in terms of x:
y = 2000 - x
Substituting this into the second equation, we get:
0.07x + 0.02(2000 - x) = 120
Simplifying this equation, we get:
0.05x + 40 = 120
Subtracting 40 from both sides, we get:
0.05x = 80
Dividing both sides by 0.05, we get:
x = 1600
So the amount invested in the mutual fund that earned 7% was $1,600. To find the amount invested in the mutual fund that earned 2%, we can use the equation:
y = 2000 - x
y = 2000 - 1600
y = 400
So the amount invested in the mutual fund that earned 2% was $400.
Let's assume the amount invested in the mutual fund that earned 7% is x dollars.
Then, the amount invested in the mutual fund that earned 2% would be (2000 - x) dollars.
The profit from the mutual fund that earned 7% would be 0.07x dollars.
The profit from the mutual fund that earned 2% would be 0.02(2000 - x) dollars.
According to the problem, the total profit was $120.
So, we can set up the equation:
0.07x + 0.02(2000 - x) = 120
Simplifying the equation:
0.07x + 40 - 0.02x = 120
0.05x + 40 = 120
0.05x = 80
x = 80 / 0.05
x = 1600
Therefore, the amount invested in the mutual fund that earned 7% was $1600.
The amount invested in the mutual fund that earned 2% was $2000 - $1600 = $400.