A small software corporation borrowed 1500 000 to expand its

A small software corporation borrowed $1,500, 000 to expand its software line. \"The corporation borrowed some of the money at 9%, some at 10%, and some at 12%. Use a system of equations to determine how much was borrowed at each rate if the annual interest rate was $ 152,000 and the amount borrowed at 10% was 2.5 times the amount borrowed at 9%. This is the updated question.

Solution

Let amount borrrowed at 9% be $ x

Let amount borrrowed at 10% be $ y

Let amount borrrowed at 12% be $ z

the amount borrowed at 10% was 2.5 times the amount borrowed at 9% y = 2.5x

Total borrowed $ 1500,000

x +y+z = 1500,000 ----> x+2.5x +z = 1500,000

3.5x +z = 1500,000 ------ ( 1)

Total interest after 1 year = $ 152,000

S.I @ 9% = x*9*1/100 = 0.09x

S.I @ 10% = 2.5*x*10*1/100 = 0.25x

SI. @ 12% = 12*z*1/100 = 0.12z

Total interest = 152,000

0.09x + 0.25x +0.12z = 152,000

0.34x + 0.12z = 152,000-----(2)

Solving equation (1) and (2) for values of x and z

x= $ 350000 borrowed @9%

z= $275000 borrowed @12%

So, y = 1500,000 - ( 350000 + 275000) = $875000 borrowed @10%