A bank loaned out ​$11,000​, part of it at the rate of 9 % per year and the rest at 19 % per year. If the interest received in one year totaled ​$1500​, how much was loaned at 9 % question mark
How much of the ​$11,000 did the bank loan out at 9 % ?

Let's solve the problem step by step.

### Given:
- Total amount loaned: $11,000
- Interest rate for part of the loan: 9% per year
- Interest rate for the remaining part: 19% per year
- Total interest received in one year: $1,500

### Let:
- $ x $ be the amount loaned at 9%.
- $ 11,000 - x $ be the amount loaned at 19%.

### The total interest received can be expressed as:
\[
\text{Interest from } 9\% \text{ loan} + \text{Interest from } 19\% \text{ loan} = 1,500
\]

This gives us the equation:
\[
0.09x + 0.19(11,000 - x) = 1,500
\]

### Let's solve for $ x $:

\[
0.09x + 0.19(11,000) - 0.19x = 1,500
\]

\[
0.09x + 2,090 - 0.19x = 1,500
\]

\[
-0.10x + 2,090 = 1,500
\]

\[
-0.10x = 1,500 - 2,090
\]

\[
-0.10x = -590
\]

\[
x = \frac{-590}{-0.10} = 5,900
\]

So, the bank loaned out **$5,900** at 9%.

Would you like any more details or have any questions about this problem?

Here are 5 related questions to expand your understanding:
1. How much was loaned at 19%?
2. What would be the interest if the entire amount was loaned at 9%?
3. How would the interest change if the rates were reversed?
4. What if the interest received was $1,200 instead of $1,500? How much would have been loaned at 9%?
5. How much would the interest be if the entire $11,000 was loaned at 19%?

**Tip:** When dealing with word problems, always start by defining variables and setting up equations based on the given conditions.

Learn how to calculate the amounts loaned at 9% and 19% interest rates from a total loan of $11,000. This problem involves solving linear equations and applying interest calculation formulas. Suitable for students in Grades 9-12.

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