Let's denote the amount Harold invested in bonds as \( B \) and the amount he invested in stocks as \( S \). According to the problem, Harold's total investment is $30,000. Therefore, we can write the first equation as:
\[ B + S = 30,000 \]
Harold earns 6% on his bonds and 12% on his stocks, and his total profit from both investments is $2,460. Thus, the second equation can be written as:
\[ 0.06B + 0.12S = 2,460 \]
To solve these equations simultaneously, we can first express \( S \) in terms of \( B \) from the first equation:
\[ S = 30,000 - B \]
Next, we substitute \( S \) into the second equation:
\[ 0.06B + 0.12(30,000 - B) = 2,460 \]
Now, distribute the 0.12:
\[ 0.06B + 0.12 \cdot 30,000 - 0.12B = 2,460 \]
\[ 0.06B + 3,600 - 0.12B = 2,460 \]
Combine the \( B \) terms:
\[ -0.06B + 3,600 = 2,460 \]
Subtract 3,600 from both sides:
\[ -0.06B = 2,460 - 3,600 \]
\[ -0.06B = -1,140 \]
Divide by -0.06:
\[ B = \frac{-1,140}{-0.06} \]
\[ B = 19,000 \]
Therefore, Harold invested $19,000 in bonds.
harold invested $30,000 in various stocks and bonds. He earned 6% of his bonds and 12% on his stocks. If harold's total profit on both types of investments was $2,460, how much of the $30,000 did he invest in bonds?
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