Question

A small software corporation borrowed $280,000 to expand its software line. Some of the money was borrowed 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 was $28,800 and the amount borrowed at 10% was 24 times the amount borrowed at 9%. Solve the system using matrices. amount borrowed at 9% $B E amount borrowed at 10% $ amount borrowed at 12% $ Need Help? Watch It Master It Talk to a Tutor

Answer 1

solution Let a u be the amount borrowed at at be the amount borrowed at 10% z be the amount borrowed at 12% = x + y + z = 280000 - 0 Annual interest changed at Anncal interest changed at Annual interest charged at 9% = 0.09X loy = 0.67 12%. = 0.127. * 0.947 oly +0:12Z = 28,800 -@ Given . y = 2 x = 3 Y = 2.5% from Eg"- x + 2-5% +2 = 280000 - = 230000 35x+ z from Eq" - = 28,300 0.09x + (0-1)/25x) + 0.122 0-34 X 7012Z = 28,800 -

€9* © x 012 - Eg" @ 0-42 x 70/2Z = 33600 0-34% +0122 - 28,800 0.08% = 4800 X = 60000 from Eq" 3-5x + 2 = 280000 3560000) + t = 280000 210000 + 2 = 280000 Z = 70000 from Eq" X.+ y + z = 280000 60000 + y + 70000 = 280000 Y = 280000 - 130000 y = 150000 . Amount borrowed at 94. =$60,000 Amount borrowed at 10% = $150000 Amount borrowed at 124 = $70000