Jayce is thinking about goign to techinal school and getting a two year degree that will qualify him or her for 38000 a year job. he could go to work today and make 14000 a year how long will it take jayce to recover his investment if he goes to college? assume he will not work at all while in college and that he will spend 4000 a year on tuition and books.

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