an actor invest some money at 9%, and 26000 more that three time the amount at 10% the total annual interest earned from the investment is 27560 how much did he invest at each amount
If x at 9%,
.09x + .10(26000+3x) = 27650
x = 64231
To solve this problem, we need to set up two equations based on the information given.
Let's represent the amount invested at 9% as x.
According to the information given, the actor invested 26000 more than three times the amount at 10%, so the amount invested at 10% can be represented as 3x + 26000.
The first equation can be set up using the formula for simple interest:
0.09x (interest earned at 9%) + 0.10(3x + 26000) (interest earned at 10%) = 27560.
Now, let's simplify the equation:
0.09x + 0.30x + 2600 = 27560.
0.39x + 26000 = 27560.
Next, let's isolate the variable:
0.39x = 27560 - 26000.
0.39x = 1560.
To solve for x, we divide both sides of the equation by 0.39:
x = 1560 / 0.39.
x = 4000.
So, the actor invested 4000 at 9% and (3*4000 + 26000) = 26000 at 10%.
Therefore, the actor invested 4000 at 9% and 26000 at 10%.