Billy Goats invested some money in stocks and bonds. The total amount he invested was $\$165,\!000$. If he invested 4.5 times as much in stocks as he did in bonds, what was his total investment in stocks?
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 $4.5s=4.5\cdot30,\!000=\boxed{135,\!000}$ dollars.
135000
Level 5
Prealgebra
Problem: Billy Goats invested some money in stocks and bonds. The total amount he invested was $\$165,\!000$. If he invested 4.5 times as much in stocks as he did in bonds, what was his total investment in stocks?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>Let the amount invested in bonds be represented as \( x \). According to the problem, Billy Goats invested 4.5 times as much in stocks as he did in bonds. Therefore, the amount invested in stocks can be expressed as \( 4.5x \).

The total investment in both stocks and bonds is given as \( 165,000 \). This can be formulated into an equation:

\[
x + 4.5x = 165,000
\]

Combining the terms on the left side gives:

\[
5.5x = 165,000
\]

To isolate \( x \), divide both sides of the equation by 5.5:

\[
x = \frac{165,000}{5.5}
\]

Calculating the right side:

\[
x = 30,000
\]

Now that we have the amount invested in bonds, we can find the amount invested in stocks by substituting \( x \) back into the expression for stocks:

\[
4.5x = 4.5 \times 30,000
\]

Calculating this gives:

\[
4.5 \times 30,000 = 135,000
\]

Thus, the total investment in stocks is \( 135,000 \).<|END_OF_LATENT|> The final answer is $135000$.