Lillian borrows $10,000. She borrows some from her friend at 8% annual interest, twice as much as that from her bank at 9%, and the remainder from her insurance company at 5%. She pays a total of $830 of interest for the first year. How much did she borrow from the insurance company?
a.
$3000
c.
$6000
b.
$1000
d.
$2300

I know the correct answer is B, but I'm having trouble seeing how to set it up. We are supposed to use Matrices

Question

Lillian borrows $10,000.  She borrows some from her friend at 8% annual interest, twice as much as that from her bank at 9%, and the remainder from her insurance company at 5%.  She pays a total of $830 of interest for the first year.  How much did she borrow from the insurance company?
a.
$3000
c.
$6000
b.
$1000
d.
$2300

I know the correct answer is B, but I'm having trouble seeing how to set it up.  We are supposed to use Matrices

dumbcow · Answer

Interest = x*8% + 2x*9% + (10,000-3x)*5% = 830
--> .08x + .18x + 500 - .15x = 830
--> .11x = 330
--> x = 3000

amounts borrowed are 3,000 , 6000, and 1000