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?

Money borrowed from insurance company = $1000

Step-by-step explanation:

Let the money borrowed by her friend at 8% interest = x

Then the money borrowed by bank at 9% interest = 2x

Total money borrowed = $10,000

So, the money borrowed from insurance company = 10,000-(2x+x)

                                                                                     = 10,000-3x

Total interest  for the first year = $830

We have the equation,

8%(x) + 9%(2x) +5% (10,000-3x) = 830

8x+18x+50,000-15x = 83,000

11x = 83000-50000

11x = 33,000

x = $3000

Then the money borrowed insurance company = 10,000-3x

                                                                                = $1,000