Darin can purchase tile at a store for 0.79 per tile and rent a tile saw for $24. at another store, he can borrow the tile saw for free if he buys tiles there for $1.19 per tile. how many tiles must he buy for the cost to be the same at both stores?

Let us denote the number of tiles by .

In the first store, if Darin bought tiles, he would need to spend:
                        (measured in $)

In the second store, if Darin bought tiles, he would need to spend:
                        (measured in $)

For the cost to be the same at both stores, it means (measured in $)
                                          

Moving over to the left hand side and changing signs:
                                           
                                           
                                           
                                            tiles

Let's check. If he buys 60 tiles in the first store, he spends:
                              $0.79×60 + $24 = $47.40 + $24 = $71.40

If he buys 60 tiles in the second store, he spends:
                                               $1.19×60 = $71.40

∴ Darin needs to buy 60 tiles for the cost to be the same at both stores.