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Ralph Chase plans to sell a piece of property for $155000. He wants the money to be paid off in two ways - a short-term note at 11% interest and a long-term note at 9% interest. Find the amount of each note if the total annual interest paid is $15550.

Respuesta :

Solution:

According to the problem, let x the amount paid off at 11%. Then, we get the following equation:

[tex]0.11x+0.09(155000-x)=15550[/tex]

now, applying the distributive property, this is equivalent to:

[tex]0.11x+13950-0.09x=15550[/tex]

this is equivalent to:

[tex]0.02x\text{ = 15550-13950=1600}[/tex]

that is:

[tex]0.02x=1\text{600}[/tex]

solving for x, we get:

[tex]x\text{ = }\frac{1600}{0.02}=80000[/tex]

then, we get:

[tex]80000\text{ at }11\%[/tex]

and

[tex]155000-80000=\text{ 75000 at }9\%[/tex]

so that, we can conclude that the correct answer is:

[tex]80000\text{ at }11\%[/tex]

and

[tex]\text{ 75000 at }9\%[/tex]

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