The volleyball team is selling raffle tickets for $1.50 each. it wants to make at least $250 from the sales. assume everyone buys the same number of tickets. if there are 75 people at the fundraiser, what is the least number of tickets each person needs to buy to meet that goal?

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