let

x = the money invested at 9%

y = the money invested at 11%

an actor invests some money at 9% and 36000 more than three times the amount at 11% means:

y = 36,000 + 3x

the total annual interest earned form the investment is 37,560:

0.09x + 0.11y = 37,560

plug y = 36,000 + 3x into the last equation

0.09x + 0.11(36,000 + 3x) = 37,560

by solving we find

x = $80,000

click here to see the step by step solution of the system equation

y = 36,000 + 3*80,000

y = $60,000

lets check, indeed

0.09*80.000 + 0.11*60,000 = 37,560

the actor invested $80,000 at 9% and $60,000 at 11%.