Mom cant help daughter with systems of three equations

Chelsea took out three loans for a total of $120,000. Her Bank Loan was at an interest rate of 8%, the small business loan was at an interest rate of 5%, the mortgage on her house was at an interest rate of 4%. The total simple interest due on the loans in one year was $5750. The annual simple interest on the mortage was $1600 more than the interest on the bank loan. How much did she borrow from each source?

"I can only get this far"

x=bank loan

y=small bus

z=mortgage

x+y+z=120,000 first equation

.8x + .5y + .4z=5750 second equation

z=1600 + x third equation

the answers are x=$15,000 y=$35,000 z=$70,000

how did they work this out????

(Worried)