Margo can purchase tile at a store for $0.59 per tile and rent a tile saw for $28. At another store she can borrow the tile saw for free if she buys tiles there for $1.29 per tile. How many tiles must she buy for the cost to be the same at both stores?

60

Step-by-step explanation:

I dont know how to explain

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