Ivan invested his savings in two investment funds. The 3,000 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 6% profit?
Let's assume that Ivan invested x amount in Fund B.
According to the given information:
- The amount invested in Fund A is $3,000.
- The profit from Fund A is 10%, which means the return from Fund A is $3,000 * 10% = $300.
- The profit from Fund B is 3%, which means the return from Fund B is x * 3% = 0.03x.
Since the total return from both funds is 6%, we can set up the equation:
$300 + 0.03x = 0.06 * (x + $3,000)
Simplifying the equation:
$300 + 0.03x = 0.06x + $180
Moving the like terms to one side:
0.06x - 0.03x = $300 - $180
0.03x = $120
Dividing both sides of the equation by 0.03, we get:
x = $120 / 0.03
x = $4,000
Therefore, Ivan invested $4,000 in Fund B.
To find out how much Ivan invested in Fund B, we can use a system of equations.
Let's assume Ivan invested x amount in Fund B.
The 3,000 he invested in Fund A returned a 10% profit, so the profit from Fund A is (3,000 * 10%) = 300.
The amount he invested in Fund B returned a 3% profit, so the profit from Fund B is (x * 3%).
Both funds together returned a 6% profit, so the total profit is ((3,000 + x) * 6%).
From the given information, we can set up the equation:
300 + (x * 3%) = (3,000 + x) * 6%
Now, let's solve the equation for x.
First, convert the percentages to decimal form:
300 + (0.03x) = (3,000 + x) * 0.06
Distribute on the right side:
300 + (0.03x) = 180 + 0.06x
Rearrange the terms:
0.03x - 0.06x = 180 - 300
Combine like terms:
-0.03x = -120
Divide both sides by -0.03 to solve for x:
x = -120 / -0.03
Simplifying:
x = 4,000
Therefore, Ivan invested $4,000 in Fund B.
(3000 * .10) + (B * .03) = .06 * (3000 + B)
300 + .03 B = 180 + .06 B