an investor invested a total of 2,000 in two mutual funds. One fund earned a 7% profit while the other earned a 5% profit. If the investors total profit was $138, How much was invested in each mutual fund
plz help
amount invested at 7% --- x
amount invested at 5% --- y
x + y = 2000
y = 2000 - x
.07x + .05(2000-x) = 138
multiply each term by 100
7x + 5(2000-x) = 13800
2x = 3800
x = 1900
so $1900 at 7% and $100 at 5%
check: .07(1900) + .05(100) = 138 , all is good
To solve this problem, let's assign variables to the amounts invested in each mutual fund.
Let "x" represent the amount invested in the fund that earned a 7% profit.
Therefore, "2000 - x" represents the amount invested in the fund that earned a 5% profit.
Since we know that the total profit earned by the investor is $138, we can set up the following equation:
0.07x + 0.05(2000 - x) = 138
Now, let's solve this equation step-by-step:
0.07x + 0.05(2000 - x) = 138
0.07x + (0.05 * 2000) - (0.05 * x) = 138
0.07x + 100 - 0.05x = 138
0.07x - 0.05x = 138 - 100
0.02x = 38
Dividing both sides of the equation by 0.02:
x = 38 / 0.02
x = 1900
Therefore, the investor invested $1900 in the mutual fund that earned a 7% profit, and $100 in the mutual fund that earned a 5% profit.
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the amount invested in the mutual fund that earned a 7% profit is X. Since the total amount invested in both funds is $2000, the amount invested in the other fund (earning a 5% profit) can be expressed as $2000 - X.
We know that the profit earned from the first fund is 7% of X, which is 0.07X. Similarly, the profit earned from the second fund is 5% of ($2000 - X), which is 0.05(2000 - X).
According to the problem, the total profit earned from both funds is $138. So, we can set up the equation:
0.07X + 0.05(2000 - X) = 138
Let's solve this equation to find the value of X.
0.07X + 0.05(2000 - X) = 138
0.07X + 100 - 0.05X = 138
0.02X = 138 - 100
0.02X = 38
Dividing both sides of the equation by 0.02, we get:
X = 38 / 0.02
X = 1900
Therefore, the investor invested $1900 in the mutual fund that earned a 7% profit and $2000 - $1900 = $100 in the mutual fund that earned a 5% profit.