Linear Equation Word Problem

Question

Cody westmoreland wishes to sell a piece of property for $240000. He wants the money to be paid off in 2 ways-- a short term note at 2% interest, and a long term note at 2.5% interest. Find the amount of each note if the total annual interest paid is $5500

Answer 1

Since it appears to be a fixed interest payment, we must assume simple interest.

Simple interest is calculated by the equation I = Prt, principle * rate * time.

 

P₁(.02)1 + P₂(.025)1 = 5500

P₁ + P₂ = 240000

 

This system is most easily solved by elimination. Multiply the top equation by -50 and then add the two equations.

 

-P₁ - 1.25P₂ = -275000

 P₁  +     P₂  =  240000

-----------------------------------

-.25P₂ = -35000

 

     P₂ = 140000

     P₁ = 100000