A bank loaned out $19000 part of it at the rate of 6% per year and the rest 14% per year. If interest received in one year totaled $1500, how much was loaned at 6%? How much of the $19000 did the bank loan out at 6%?

Let's define the amounts loaned out at each interest rate.

Let:
- $ x $ be the amount loaned at 6%.
- $ 19000 - x $ be the amount loaned at 14%.

### Step 1: Interest Earned
The interest earned from the loan at 6% is:
\[
\text{Interest from 6% loan} = 0.06x
\]

The interest earned from the loan at 14% is:
\[
\text{Interest from 14% loan} = 0.14(19000 - x)
\]

### Step 2: Total Interest
The total interest earned in one year is $1500. So, we can set up the following equation:
\[
0.06x + 0.14(19000 - x) = 1500
\]

### Step 3: Solve the Equation
First, expand the equation:
\[
0.06x + 0.14(19000) - 0.14x = 1500
\]

Simplify:
\[
0.06x + 2660 - 0.14x = 1500
\]

Combine like terms:
\[
-0.08x + 2660 = 1500
\]

Subtract 2660 from both sides:
\[
-0.08x = 1500 - 2660
\]
\[
-0.08x = -1160
\]

Divide by -0.08:
\[
x = \frac{-1160}{-0.08} = 14500
\]

### Final Answer:
The bank loaned out **$14,500** at 6%. The rest, $ 19000 - 14500 = 4500 $, was loaned out at 14%.

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Would you like more details or have any questions? 

Here are some related questions to explore:
1. How would the answer change if the total interest were $2000?
2. What if the amount loaned at 14% was higher than the amount at 6%?
3. Can you calculate the interest earned separately for each loan amount?
4. What is the total interest earned over 2 years?
5. How much would the total interest be if the rates were swapped?

**Tip:** Always check units (like percentages and dollar amounts) when setting up your equations to avoid mistakes.

A bank loaned out $19000, part of it at the rate of 6% per year and the rest at 14% per year. If interest received in one year totaled $1500, how much was loaned at 6%?

This math problem involves calculating the amounts loaned at different interest rates. Learn how to solve a linear equation to determine how much of the $19000 was loaned at 6%, using simple interest formulas. A step-by-step solution is provided for students in Grades 9-11.

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