Question

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.

Answer 1

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

`0.11x+0.09(155000-x)=15550`

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

`0.11x+13950-0.09x=15550`

this is equivalent to:

`0.02x\text{ = 15550-13950=1600}`

that is:

`0.02x=1\text{600}`

solving for x, we get:

`x\text{ = }(1600)/(0.02)=80000`

then, we get:

`80000\text{ at }11\%`

and

`155000-80000=\text{ 75000 at }9\%`

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

`80000\text{ at }11\%`

and

`\text{ 75000 at }9\%`