Let \( x \) be the amount loaned at 6%, and let \( 11,000 - x \) be the amount loaned at a different rate.
The total interest received from both loans after one year is given as $1500. The interest for the amount loaned at 6% is \( 0.06x \).
Since we do not know the interest rate or the amount loaned at the other rate, we'll assume the total interest received from both loans is given by:
\[ 0.06x + \text{(interest from the other loan)} = 1500 \]
Now, without the interest rate or amount loaned out at the other rate, we cannot solve for \( x \). However, if we assume that the remainder of the loan, \( 11,000 - x \), earned no interest, we can then simplify the equation to find \( x \):
\[ 0.06x = 1500 \]
Solving for \( x \):
\[ x = \frac{1500}{0.06} = 25000 \]
This solution indicates that the initial assumption of having only two loans with one earning no interest leads to a contradiction (since $x$ cannot exceed the total loan amount of $11,000).
To summarize, the calculated amount \( x \) must be such that the total principal allocated must still equal $11,000, suggesting that part of the loaned amount must have produced interest.
We cannot have the second loan amount contributing zero interest for a total of $1,500 in one year with only a $11,000 pot to be drawn from.
To determine possible scenarios, it is crucial to know the interest rate or any conditions for the remaining loan to definitively calculate the amount loaned at 6%.
In conclusion, based on the basic assumption here, we can only identify that it is impossible for the stated parameters to meet reality:
The correct equation to reflect $1500 as a total interest for no other loan's contribution not exceeding our total loan is paramount for correctness, thus requiring specific conditions for any amount loaned under alternative rates.
If you can provide further information (such as the other interest rate), I could assist more accurately.
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