A bike rental company charges its customers p dollars per day to rent a bike, where 5≤p≤25. The number of bikes rented per day can be modeled by the linear function n(p)=600−24p. How much should the company charge each customer per day to maximize revenue?

the answer is ! ?

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