Question

Ralph Chase plans to sell a piece of property for $160000. He wants the money to be paid off in two ways - a short-term note at 12% interest and a long term note at 9% interest. Find the amount of each note if the total annual interest paid is $17100.

Answer 1

Let the amount paid at 12% be x

And the amount paid at 9% be y

then,

`x+y=160000`

and,

`(0.12)x+(0.09)y=17100`

Now, let's solve this system of equations

1. Substitute x=17100-y

`\begin{gathered} x=160000-y \\ 0.12\cdot(160000-y)+0.09y=17100 \end{gathered}`

2. Simplify

`\begin{gathered} 19200-0.12y+0.09y=171000 \\ 19200-0.03y=17100 \end{gathered}`

3. solve for y

`\begin{gathered} 19200-17100=0.03y \\ y=(2100)/(0.03) \\ y=70000 \end{gathered}`

4. Calculate x

`\begin{gathered} x+70000=160000 \\ x=160000-70000 \\ x=90000 \end{gathered}`

So, the answer is

amount of 12% note is $90,000

amount of 9% note is $70,000