Question

you will see a few examples of applications to practice with. your real test will have a test bank that will pull one question of any type.
a bank loaned out $20,500, part of it at the rate of 11% annual interest, and the rest at 13% annual interest. the total interest earned for both loans was $2,465.00. how much was loaned at each rate?
$______ was loaned at 11% and
$______ was loaned at 13%.

Explanation:

Step1: Define variables for each loan

Let $x$ = amount loaned at 11%, $20500 - x$ = amount loaned at 13%.

Step2: Set up interest equation

Total interest = 11% of $x$ + 13% of $(20500 - x)$
$$0.11x + 0.13(20500 - x) = 2465$$

Step3: Expand and simplify the equation

$$0.11x + 2665 - 0.13x = 2465$$
$$-0.02x + 2665 = 2465$$

Step4: Solve for $x$

$$-0.02x = 2465 - 2665$$
$$-0.02x = -200$$
$$x = \frac{-200}{-0.02} = 10000$$

Step5: Find the 13% loan amount

$$20500 - x = 20500 - 10000 = 10500$$

Answer:

$10,000 was loaned at 11% and
$10,500 was loaned at 13%.