Carlos invested his savings in two investment funds. The $2000 that he invested in Fund A returned a 10% profit. The amount that he invested in Fund B returned a 3% profit. How much did he invest in Fund B, if both funds together returned a 5% profit?
0.03B + 0.10(2000-B) = 0.05 * 2000
Let's assume that Carlos invested x dollars in Fund B.
According to the information given, the amount Carlos invested in Fund A is $2000, and it returned a 10% profit. This means that the profit from Fund A is 10% of $2000, which is (10/100) * $2000.
The amount Carlos invested in Fund B returned a 3% profit. This means that the profit from Fund B is 3% of x dollars, which is (3/100) * x.
The total profit from both funds is 5% of the total amount invested. So, the total profit is (5/100) * (2000 + x).
Since the total profit is the sum of the individual profits, we can set up an equation:
(10/100) * $2000 + (3/100) * x = (5/100) * (2000 + x)
To solve for x, let's simplify the equation:
(10/100) * $2000 + (3/100) * x = (5/100) * (2000 + x)
(10/100) * 2000 + (3/100) * x = (5/100) * 2000 + (5/100) * x
200 + (3/100) * x = 100 + (5/100) * x
(3/100) * x - (5/100) * x = 100 - 200
(-2/100) * x = -100
x = (-100) / (-2/100)
x = (-100) * (100/2)
x = $5000
Therefore, Carlos invested $5000 in Fund B.
To solve this problem, we need to set up an equation based on the given information.
Let's consider the amount Carlos invested in Fund B as 'x'.
Carlos invested $2000 in Fund A, which returned a 10% profit. So, the profit from Fund A can be calculated as follows: 10% of $2000 = $200.
Carlos also invested 'x' amount in Fund B, which returned a 3% profit. So, the profit from Fund B can be calculated as follows: 3% of 'x' = 0.03x.
According to the problem, the combined profit from both funds is 5% of the total investment amount. So, the total profit can be calculated as follows: 5% of ($2000 + 'x') = 0.05 * ($2000 + 'x').
Now we can set up the equation:
Profit from Fund A + Profit from Fund B = Total Profit
$200 + 0.03x = 0.05 * ($2000 + x)
Now, let's solve the equation to find the value of 'x':
$200 + 0.03x = 0.05 * ($2000 + x)
200 + 0.03x = 0.05 * $2000 + 0.05 * x
200 + 0.03x = $100 + 0.05x
0.03x - 0.05x = $100 - $200
-0.02x = -$100
x = -$100 / -0.02
x = $5000
Therefore, Carlos invested $5000 in Fund B.