Ralph Chase plans to sell a piece of property for $170000. He wants the money to be paid off in two ways - a short-term note at 10% interest and a long-term note at 7% interest. Find the amount of each note if the total annual interest paid is $14750.

This problem involves a system of linear equations. The two equations are derived from the total property value and the total interest. They can be solved using either the substitution or the elimination method to determine the amounts of the short-term and long-term notes.

Explanation:

This problem is an example of a system of linear equations. We know that the total property value is $175,000 and it is divided into a short-term note and a long-term note. Let's represent the short-term note's value as x and the long-term note's value as y. Thus, the first equation can be written as x + y = 175,000.

The second equation comes from the total interest earned, which is $17,650. The interest from the short-term note is 11% of its value, or 0.11x, and the interest from the long-term note is 9% of its value, or 0.09y. This gives us the equation 0.11x + 0.09y = 17,650.

Now we can solve these equations using substitution or elimination method. Results will give the values of x and y, which represent the amounts of the short-term note and the long-term note, respectively.