Question

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?

Answer 1

Let us denote the number of tiles by $T$.

In the first store, if Darin bought $T$ tiles, he would need to spend:
                        $0.79\times T+24$ (measured in $)

In the second store, if Darin bought $T$ tiles, he would need to spend:
                        $1.19\times T$ (measured in $)

For the cost to be the same at both stores, it means (measured in $)
                                           $1.19T=0.79T+24$

Moving $0.79T$ over to the left hand side and changing signs:
                                            $1.19T-0.79T=24$
                                            $0.4T=24$
                                            $T= \frac{24}{0.4}$
                                            $T=60$ 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.