Question

Ralph chase plans to sell a piece of property for $145000. He wants the money to be paid off in two ways- and short term note at 9% and a long term note at 7% interest. Find the amount of each note if the total anual interest paid is $11650

Answer 1

Let's denote the amount of the short-term note as x and the amount of the long-term note as y. We know that:

1. The total amount of the property is $145,000, so x + y = $145,000.

2. The total annual interest is $11,650, which is the sum of the interest from the short-term note (9% of x) and the long-term note (7% of y). So, 0.09x + 0.07y = $11,650.

We now have a system of two equations that we can solve to find the values of x and y.

Let's solve this system of equations:

1. Multiply the first equation by 0.07: 0.07x + 0.07y = $10,150.

2. Subtract this from the second equation: 0.02x = $1,500.

3. Solve for x: x = $1,500 / 0.02 = $75,000.

Substitute x = $75,000 into the first equation to find y:

$75,000 + y = $145,000

y = $145,000 - $75,000 = $70,000.

So, the short-term note is $75,000, and the long-term note is $70,000.