Interest Rate word problem

Question

A small corporation borrowed $774,000 to expand its clothing line. Some of the money was borrowed at 8%, some at 9%, and some at 10%. How much was borrowed at each rate if the annual interest owed was $67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%?

Answer 1

Let x be the amount borrowed at 8%

      y                                       at 9%

      z                                       at 10%

 

Then the total interest paid can be calculated by the equation

 

1.  x*0.08+y*0.09+z*0.1=67500

 

also it is said that

 

2.  x=4z ( amount borrowed at 8% was four times the amount borrowed at 10%)

 

the total amount borrowed

 

3.  x+y+z=774000

 

now we have three equations

 

let substitute x for 4z in 3rd equation

 

4z+y+z=774000

 

y+5z=774000

 

y=774000-5z

 

 

let substitute  

x for 4z and y=774000-5z into first equation

 

4z*0.08+(774000-5z)*0.09+z*0.1=67500

 

let solve this equation

 

0.32z+69660-0.45z+0.1z=67500

 

-0.03z=-2160

 

z=-2160/-0.03=$72000

 

x=4z=72000*4=$288000

 

y=774000-5z=774000-72000*5=$414000