jmc

Let the amount of money Billy invested in bonds be $s.$ Then, the amount of money he invested in stocks is $4.5s.$ The total amount of money he invested is $s+4.5s=5.5s=165,000.$ Thus, $s=\frac{165,000}{5.5}=30,000.$ Finally, the amount invested in stocks is $4.5s=4.5\cdot 30,000=\boxed{135,000}$ dollars.