A bank loaned out ​$14,000​, part of it at the rate of 9 % per year and the rest at 17 % per year. If the interest received in one year totaled ​$2000​, how much was loaned at 9 % question mark
How much of the ​$14,000 did the bank loan out at 9 % question mark

Let's solve this problem by setting up a system of equations based on the given information.

Let:
- $ x $ be the amount loaned at 9%.
- $ y $ be the amount loaned at 17%.

We know the following:
1. The total amount loaned is $14,000:
   \[
   x + y = 14,000
   \]

2. The total interest received in one year is $2,000. The interest earned from the amounts loaned at 9% and 17% can be represented as:
   \[
   0.09x + 0.17y = 2,000
   \]

Now, let's solve this system of equations.

### Step 1: Solve the first equation for $ y $:
\[
y = 14,000 - x
\]

### Step 2: Substitute $ y $ in the second equation:
\[
0.09x + 0.17(14,000 - x) = 2,000
\]

Simplify and solve for $ x $:
\[
0.09x + 0.17 \times 14,000 - 0.17x = 2,000
\]
\[
0.09x + 2,380 - 0.17x = 2,000
\]
\[
-0.08x + 2,380 = 2,000
\]
\[
-0.08x = 2,000 - 2,380
\]
\[
-0.08x = -380
\]
\[
x = \frac{380}{0.08}
\]
\[
x = 4,750
\]

So, the amount loaned at 9% is **$4,750**.

### Amount loaned at 17%:
\[
y = 14,000 - 4,750 = 9,250
\]

So, the amount loaned at 17% is **$9,250**.

**Summary**:
- Amount loaned at 9%: $4,750
- Amount loaned at 17%: $9,250

Would you like more details or have any other questions?

### Related Questions:
1. What would be the interest if the entire $14,000 was loaned at 9%?
2. How would the total interest change if the rates were switched between the amounts?
3. What is the percentage of the total amount loaned at 9%?
4. How much interest would be received if $10,000 were loaned at 9% and the rest at 17%?
5. How would the total interest change if the loan periods were different?

**Tip**: Always double-check your calculations by substituting back into the original equations to ensure the solution is correct!

Learn how to calculate how much of a $14,000 loan was distributed at 9% and 17% interest rates, given a total interest of $2,000 per year. Includes step-by-step solution and formulas for linear equations and interest calculation. Suitable for students in Grades 9-12.

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