Cynthia's credit card has a limit of $1,000 with an introductory rate of 0%, a late fee of $35, and currently a balance of $0. the card also has an annual fee of $45 which is applied every year in august. cynthia makes a $75 purchase that shows up on her august bill and she pays $45 before the due date. what will be the balance on cynthia's credit card?
$45
$65
$35
$75

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