Question

Ralph Chase plans to sell a piece of property for $175000. He wants the money to be paidth the amount of each note if the total annual interest paid is $15900off in two ways - a short-term note at 10% interest and a long-term note at 8% interest. Find the amount of each note if the total annual interest paid is $15900

Answer 1

From the given information, we know that the sum of the interest must be equal to the total annual interest of $15,000. So, we can write

`0.10x+0.08(175000-x)=15,900`

where x denotes the amount of money at 10% and (175000 -x) the amount of money at 8%. Then, our last equation is equivalent to

`0.10x-0.08x+14000=15,900`

Then, by subtracting 14000 to both sides, we have

`0.10x-0.08x=1,900`

and by collecting the terms on the left hand sides, we have

`0.02x=1,900`

Now, by dividing both sides by 0.02, we obtain

`\begin{gathered} x=(1,900)/(0.02) \\ x=95,000 \end{gathered}`

Then, $95,000 is the amount paid off at 10%.

Now, by substituting this result into (175000 -x), which corresponds to the amount paid off at 8%, we get

`175,000-95,000=80,000`

Therefore, the answer is: $95,000 amount paid off at 10% and $80,000 amount paid off at 8%