Juan borrows $100,000 to pay for medical school. he borrows part of the money from the school whereby he will pay 4.5% simple interest. he borrows the rest of the money through a government loan that will charge him 6% interest. in both cases, he is not required to pay off the principal or interest during his 4 yr of medical school. however, at the end of 4yr, he will owe a total of $19,200 for the interest from both loans. how much did he borrow from each source?

Let the amount Juan borrows from the from school be x, and the amount borrowed in government be y.
Total amount of money will be:
x+y=100,000
x=100,000-yi
given that the interest charged from the money is simple interest, the amount of interest charged from x will be:
interest=(PRT)/100
=(x×4.5×4)/100
=0.18x

interest charged in y will be:
(y×6x4)/100
=0.24y
therefore the total interest will be:
0.18x+0.24y=19200ii
substituting i in ii we get:
0.18(100000-y)+0.24y=19200
18000-0.18y+0.24y=19200
0.24y-0.18y=19200-18000
0.06y=1200
y=1200/0.06
y=20,000
x=10000-20000
x=80,000
therefore he borrowed $80,000 from school and $20,000 from government.