Question

a bank loaned out $13,000, 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 $1500, how much was loaned at 9%?
how much of the $13,000 did the bank loan out at 9%?
$

Explanation:

Step1: Define Variables

Let $x$ be the amount loaned at 9%, so the amount loaned at 17% is $13000 - x$.

Step2: Set Up Interest Equation

The interest from 9% loan is $0.09x$, and from 17% loan is $0.17(13000 - x)$. Total interest is $1500$, so:
$$0.09x + 0.17(13000 - x) = 1500$$

Step3: Solve the Equation

Expand: $0.09x + 2210 - 0.17x = 1500$
Combine like terms: $-0.08x + 2210 = 1500$
Subtract 2210: $-0.08x = 1500 - 2210 = -710$
Divide by -0.08: $x = \frac{-710}{-0.08} = 8875$

Answer:

$\$8875$