Anne and justin each opened a saving account in the same day. anne started by putting $679 in her account , and she will deposit an additional $262 each week . justin made an initial deposit of $685, and will add $259 more each week. eventually , anne and justin will each have the same amount saved . what is that amount ? how many weeks will that take ?

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