Sarah ordered 2 posters and 4 movies for $109.94. Adam bought 3 posters and 2 movies for $84.95. If all posters are the same price, and all movies are the same price, how much is a single poster and how much is a single movie?

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

the answer would be a 24

step-by-step explanation:

c=2πr=2·π·3=24

the correct answer would be the third option