An investor invested a total of $2,600 in two mutual funds. One fund earned a 5% profit while the other earned a 3% profit. If the investor's total profit was $98, how much was invested in each mutual fund?

The amount invested in the mutual fund that earned 5% was $ ?

The amount invested in the mutual fund that earned 3% was $ ?

$X @ 3%.

$(2600-x) @ 5%.

0.03x + 0.05(2600-x) = $98.
0.03x + 130-0.05x = 98
-0.02x = 98-130 = -32
X = $1600 @ 3%.
2600-x = 2600-1600 = $1000. @ 5%.

To solve this problem, let's assign variables to the unknowns:

Let x be the amount invested in the mutual fund that earned a 5% profit (in dollars).
Let y be the amount invested in the mutual fund that earned a 3% profit (in dollars).

From the given information, we know two things:

1. The total amount invested in both mutual funds is $2,600.
This can be written as:
x + y = 2600

2. The total profit earned from both mutual funds is $98.
This can be written as:
0.05x + 0.03y = 98

Now we have a system of two equations with two variables. We can solve this system using various methods, such as substitution or elimination. Let's solve it using the substitution method.

First, we'll solve the first equation for y:
y = 2600 - x

Now substitute this value of y into the second equation:
0.05x + 0.03(2600 - x) = 98

Distribute 0.03:
0.05x + 78 - 0.03x = 98

Combine like terms:
0.02x + 78 = 98

Subtract 78 from both sides:
0.02x = 20

Divide both sides by 0.02:
x = 1000

So, the amount invested in the mutual fund that earned a 5% profit is $1,000.

To find the amount invested in the mutual fund that earned a 3% profit, substitute the value of x into the first equation:
1000 + y = 2600

Subtract 1000 from both sides:
y = 1600

Therefore, the amount invested in the mutual fund that earned a 3% profit is $1,600.