With income earned by selling the rights to his life story, an actor invests some of the money at 3% and 30,000 more than twice as much at 4%. The total annual interest earned from the investments is $5600. How much is invested at each rate?
let the amount invested at 3% be x
then the amount invested at 4% = 2x+30000
solve for x
.03x + .04(2x+30000) = 5600
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To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the actor invests an amount x at 3% and invests an amount (2x + 30000) at 4%.
The interest earned from the 3% investment is then (x * 0.03), and the interest earned from the 4% investment is ((2x + 30000) * 0.04).
We are told that the total interest earned from both investments is $5600. So we can set up the equation:
0.03x + 0.04(2x + 30000) = 5600
Now let's solve the equation step by step:
First, distribute 0.04 to (2x + 30000):
0.03x + 0.08x + 1200 = 5600
Combine like terms:
0.11x + 1200 = 5600
Next, subtract 1200 from both sides of the equation:
0.11x = 4400
Divide both sides by 0.11 to solve for x:
x = 4400 / 0.11
x = 40000
So the actor invested $40,000 at 3% and (2 * 40000 + 30000) = $110,000 at 4%.
Therefore, the actor invested $40,000 at 3% and $110,000 at 4%.