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?

Let x be the amount borrowed from the bank. Then Lillian borrowed 2x from her friend and $10,000 − 3x from the insurance company. The first-year interest is 0.09x + 0.08(2x) + 0.05($10,000 − 3x) = $830, which simplifies to $500 + 0.10x = $830. Thus x = $3,300, so the insurance-company loan was $10,000 − 3($3,300) = $1,000, choice b.

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