Goran invested his savings in two investment funds. The amount he invested in fund A was$2000 less than the amount he invested in fund B. Fund A returned a 3% profit and fund B returned a 2% profit. How much did he invest in fund A, if the total profit from the two funds together was $540
Let X be the amount Goran invested in fund B. So in fund A, he invested X-2000 dollars.
Fund A returned 0.03(X-2000) and fund B returned 0.02X in profit.
The sum of the returns is $540: 0.03(X-2000)+0.02X = 540.
Combining the like terms, we get 0.05X - 60=540.
Adding 60 to both sides, we get 0.05X = 600
Dividing both sides by 0.05, we get X = <<12000=12000>>12,000.
Goran invested X-2000 = 12000-2000 = $<<12000-2000=10000>>10,000 in fund A. Answer: \boxed{10000}.
To find out how much Goran invested in Fund A, we can set up equations based on the given information.
Let's assume Goran invested x dollars in Fund B.
According to the problem, the amount invested in Fund A is $2000 less than Fund B. Therefore, the amount Goran invested in Fund A would be x - $2000.
Now, let's calculate the profits earned from each investment:
Profit from Fund A = (x - $2000) * 3% = 0.03(x - $2000)
Profit from Fund B = x * 2% = 0.02x
The total profit from both funds is $540. So, we can write the equation:
0.03(x - $2000) + 0.02x = $540
Now, let's solve this equation to find the value of x (the amount invested in Fund B):
0.03x - $60 + 0.02x = $540
0.05x - $60 = $540
0.05x = $540 + $60
0.05x = $600
Dividing both sides by 0.05:
x = $600 / 0.05
x = $12,000
Therefore, Goran invested $12,000 in Fund B.
To find out how much Goran invested in Fund A, we substitute the value of x into our equation:
Amount invested in Fund A = $12,000 - $2000 = $10,000
So, Goran invested $10,000 in Fund A.
Let's denote the amount Goran invested in fund B as "x" dollars. According to the information given, the amount he invested in fund A is $2000 less than the amount he invested in fund B. Therefore, the amount invested in fund A is (x - $2000) dollars.
The profit earned from fund A is calculated by multiplying the amount invested in fund A by the profit rate:
Profit from fund A = (x - $2000) * 3/100
The profit earned from fund B is calculated by multiplying the amount invested in fund B by the profit rate:
Profit from fund B = x * 2/100
The total profit from the two funds is $540, so we can set up the equation:
(x - $2000) * 3/100 + x * 2/100 = $540
Now, let's solve this equation to find the value of x, i.e., the amount Goran invested in fund B:
(3/100)x - (3/100)($2000) + (2/100)x = $540
Simplifying the equation:
(3/100)x + (2/100)x - $60 + $40 = $540
(5/100)x = $540 + $60 - $40
(5/100)x = $560
Dividing both sides by (5/100):
x = $560 / (5/100)
x = $560 * (100/5)
x = $11200
Therefore, Goran invested $11200 in fund B.
To find the amount Goran invested in fund A, we subtract $2000 from the amount invested in fund B:
Amount invested in fund A = $11200 - $2000 = $9200
So, Goran invested $9200 in fund A.