Thread: 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????

Originally Posted by 2HotNAZ

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 Mr F says: 8% is the same as 8/100 = 0.08 etc. So the equation should be .08x + .05y + .04z=5750.

z=1600 + x third equation Mr F says: This equation is about the interest, not the amount borrowed. So it should be 0.04z = 1600 + 0.08x.

the answers are x=$15,000 y=$35,000 z=$70,000
how did they work this out????

So the correct equations to solve are:

x + y + z =120,000 .... (1)

.08x + .05y + .04z = 5750 .... (2)

0.04z = 1600 + 0.08x .... (3)

Originally Posted by mr fantastic

So the correct equations to solve are:

x + y + z =120,000 .... (1)

.08x + .05y + .04z = 5750 .... (2)

0.04z = 1600 + 0.08x .... (3)

now wonder youre name is Mr. Fantastic!