Let us denote the number of tiles by [tex]T[/tex].
In the first store, if Darin bought [tex]T[/tex] tiles, he would need to spend:
[tex]0.79\times T+24[/tex] (measured in $)
In the second store, if Darin bought [tex]T[/tex] tiles, he would need to spend:
[tex]1.19\times T[/tex] (measured in $)
For the cost to be the same at both stores, it means (measured in $)
[tex]1.19T=0.79T+24[/tex]
Moving [tex]0.79T[/tex] over to the left hand side and changing signs:
[tex]1.19T-0.79T=24[/tex]
[tex]0.4T=24[/tex]
[tex]T= \frac{24}{0.4} [/tex]
[tex]T=60[/tex] 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.
