An investor invested a total of 2900 in two mutual funds. One fund earned a 9% profit the other earned a 5% profit. If the investors total profit was $217 how much was invested in each mutual fund.

To solve this problem, we can set up a system of two equations based on the given information.

Let's assume the amount invested in the mutual fund that earned a 9% profit is x, and the amount invested in the mutual fund that earned a 5% profit is y.

According to the given information, the total amount invested is $2900. Therefore, we have our first equation:

x + y = 2900 --(1)

Additionally, the total profit earned from both investments is $217. To calculate the profits earned from each mutual fund, we need to calculate 9% of x and 5% of y:

0.09x + 0.05y = 217 --(2)

Now, we have a system of two equations:

x + y = 2900 --(1)
0.09x + 0.05y = 217 --(2)

We can solve this system of equations simultaneously to find the values of x and y, which represent the amounts invested in each mutual fund.

There are several methods to solve this system, such as substitution, elimination, or matrix methods. Here, we'll use the substitution method:

Let's solve equation (1) for x:

x = 2900 - y

Now, substitute this value of x in equation (2):

0.09(2900 - y) + 0.05y = 217

Multiply out the equation:

261 - 0.09y + 0.05y = 217

Combine like terms:

-0.04y = -44

Divide by -0.04:

y = 1100

Now, substitute this value back into equation (1) to solve for x:

x + 1100 = 2900

x = 1800

Therefore, $1800 was invested in the mutual fund that earned a 9% profit, and $1100 was invested in the mutual fund that earned a 5% profit.