Larry loves music. He bought $285 worth of MP3 files
on his credit card, and now he
cannot afford to pay off his debt.
If the credit-card company
charges him 18% annual interest
compounded monthly, how does
Larry's debt grow as time
passes? How much would he
owe at the end of the year if he
had a "no payments for 12
months" feature for his credit
card?

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4