Let [tex]x_1[/tex] be the amount of money invested at 7% and [tex]x_2[/tex] the amount of money invested at 11%. The actor invests [tex]x_1[/tex] at 7% and 25000$ more than [tex]2x_1[/tex] at 11%, it means:
[tex]2x_1+25000=x_2[/tex] (Equation 1)
The total annual interest earned is 45670$:
[tex]\frac{7}{100}x_1+\frac{11}{100}x_2=45670[/tex] (Equation 2).
We remove [tex]x_2[/tex] from equation 2 by using equation 1:
[tex]\frac{7}{100}x_1+\frac{11}{100}(2x_1+25000)=45670\\
7x_1+22x_1+275000 = 4567000\\
29x_1 = 429200\\
x_1 = 4292000/29 = 148000\\
x_2 = 2x_1+25000 = 321000\\[/tex]
He invests 148000$ at 7% and 321000$ at 11%.
