The amount of the ​11% note is? And The amount of the 9% note is?

Question

Ralph Chase plans to sell a piece of property for

​$180000. 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 ​$18200.

Answer 1

Let x and y be the two amounts

0.11x + 0.09y = 18200

Scaling by 100

11x + 9y = 1820000 Eqn 1

x + y = 180000 Eqn 2

Multiplying Eqn 2 by 9 and subtracting from Eqn 1, gives:

2x = 200000

x = $100000

y = $80000