Solve analytically A small cooperation borrowed 775000 to ex

Solve analytically. A small cooperation borrowed $775,000 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 when the annual interest owed was $67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%.

Solution

Some of the money was borrowed at 8% ( let it be x ) , some at 9%( let it be y) ,

and some at 10% (let it be z) .

small cooperation borrowed $775,000 : x +y +z = $775,000 ----(1)

annual interest owed was $67,500 : 0.08x + 0.09y +0.1z = $67,500 ----(2)

amount borrowed at 8% was four times the amount borrowed at 10%. : x = 4z

x -4z =0 -----(3)

Solve equations 1 , 2 , 3 to solve for x , y , z :

On solving we get x = $300,000 invested at 8%

y =$400,000 invested at 9%

z =$75000 invested at 10%