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.

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BlakelynW475933 BlakelynW475933 · Answer 1 · 2022-11-03T05:06:35+01:00

Let the amount paid at 12% be x

And the amount paid at 9% be y

then,

[tex]x+y=160000[/tex]

and,

[tex](0.12)x+(0.09)y=17100[/tex]

Now, let's solve this system of equations

1. Substitute x=17100-y

[tex]\begin{gathered} x=160000-y \\ 0.12\cdot(160000-y)+0.09y=17100 \end{gathered}[/tex]

2. Simplify

[tex]\begin{gathered} 19200-0.12y+0.09y=171000 \\ 19200-0.03y=17100 \end{gathered}[/tex]

3. solve for y

[tex]\begin{gathered} 19200-17100=0.03y \\ y=\frac{2100}{0.03} \\ y=70000 \end{gathered}[/tex]

4. Calculate x

[tex]\begin{gathered} x+70000=160000 \\ x=160000-70000 \\ x=90000 \end{gathered}[/tex]

So, the answer is

amount of 12% note is $90,000

amount of 9% note is $70,000