Let \( x \) be the amount Rosalinda invested in the 6% bonds. Therefore, the amount she invested in the 10% bonds would be \( 15000 - x \).
According to the problem, the profit on the 10% bonds was $1,000 more than the profit on the 6% bonds.
The profit from the 6% bonds can be expressed as: \[ 0.06x \]
The profit from the 10% bonds can be expressed as: \[ 0.10(15000 - x) \]
According to the information given: \[ 0.10(15000 - x) = 0.06x + 1000 \]
Now, let's solve this equation step by step:
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Expand the left side: \[ 1500 - 0.10x = 0.06x + 1000 \]
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Rearranging this gives: \[ 1500 - 1000 = 0.06x + 0.10x \] \[ 500 = 0.16x \]
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Now, solve for \( x \): \[ x = \frac{500}{0.16} = 3125 \]
Therefore, Rosalinda invested \( \boxed{3125} \) dollars in the 6% bonds.
To verify:
- Amount invested in 10% bonds = \( 15000 - 3125 = 11875 \)
- Profit from 6% bonds = \( 0.06 \times 3125 = 187.5 \)
- Profit from 10% bonds = \( 0.10 \times 11875 = 1187.5 \)
Now, check the condition: The profit on the 10% bonds is \( 1187.5 \), which is indeed \( 1000 \) more than the profit on the 6% bonds (\( 187.5 + 1000 = 1187.5 \)).
Thus, the solution is confirmed correct, and Rosalinda invested \( \boxed{3125} \) dollars in the 6% bonds.