Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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.

Sagot :

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

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.