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)

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)