Crystal is selling tickets for her school fair. On the first day, she sold 3 senior citizen tickets and 1 child ticket for a total of $38. On the second day, she got $52 by selling 3 senior citizen tickets. Find the price of a senior citizen ticket and the price of a child ticket.

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

step-by-step explanation:

659