Student borrowed 775,000. Some borrowed at 8%, 9% , 10%. How much borrowed at each interest rate if the annual interest was 67,500 and the amount borrowed at 8% was four times the amount borrowed at 10%?
average annual interest rate = 67500/775000=27/310 Let amount borrowed at 10% was x, then amount borrowed at 8% was 4x, and the amount borrowed at 9% was 775000-(x+4x)=775000-5x Total interest 4x(.08)+x(0.10)+(775000-5x)(0.09)=67500 Isolate x and solve -3x+6975000=6750000 3x=225000 x=75000 at 10% So 4x=75000*4=300000 at 8% 775000-5x=775000-375000=400000 at 9% Check: 300000*0.08+75000*0.10+400000*0.09=67500 (correct)
